REGULAR PAPER

Japanese Journal of Applied Physics 53, 07KF03 (2014)
http://dx.doi.org/10.7567/JJAP.53.07KF03

Correction of change in propagation time delay of pulse wave during ﬂow-mediated dilation
in ultrasonic measurement of arterial wall viscoelasticity
Mitsuki Sato1, Hideyuki Hasegawa1,2, and Hiroshi Kanai1,2*
1Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
E-mail: kanai@ecei.tohoku.ac.jp
2

Received November 29, 2013; revised January 31, 2014; accepted March 14, 2014; published online June 5, 2014
It is considered that the endothelial dysfunction occurs in the initial step of atherosclerosis. Although assessments of the endothelial function andviscoelastic properties of the intima-media region are important for the diagnosis of early-stage atherosclerosis, regional viscoelasticity has not yet
been measured in vivo. Our group has developed an ultrasonic method for measuring the transient change in viscoelasticity during ﬂow-mediateddilation (FMD). However, in this method, the stress (blood pressure) and strain of the intima-media region of the radial artery are measured indifferent arms, and the change in pulse wave velocity (PWV) due to FMD has not yet been considered. In the present study, we measured bloodpressure waveforms using two pressure sensors, which were placed along the same radial artery for the ultrasonic measurement, to obtain bloodpressure waveforms and estimate the PWV between the two sensors. Using the measured PWV, the pulse wave propagation time from thepressure sensor to the position of the ultrasound probe was corrected, and viscoelasticity was estimated from the corrected stress–strain
relationship. In the basic experiment, we applied the proposed method to a silicone tube phantom and evaluated the accuracy of the estimation ofviscoelasticity by comparing the ultrasonic measurement to the results of the tensile test. In the in vivo measurements, the change in the
propagation time delay of the pulse wave was also corrected using the two pressure sensors and the stress–strain relationship of the radial arterial
wall was then obtained to estimate viscoelasticity. Furthermore, a decrease in elasticity owing to FMD after recirculation was clearly observed, andthe unstable temporal variation in viscosity was signiﬁcantly reduced. These results demonstrated the improvement in the accuracy of themeasurement of viscoelasticity by the proposed method. © 2014 The Japan Society of Applied Physics

1.

Introduction

Cardiovascular diseases have been cited as the main cause ofdeath in Japan, and the primary cause of such diseases isatherosclerosis. The initial step in atherosclerosis is considered to be the endothelial dysfunction.1) Also, the homeostasis of a vessel wall is abrogated2) and the inﬂammation of
the inner layer is induced by atherosclerosis. Consequently, it
is important for an early preventive treatment of atherosclerosis to noninvasively assess the endothelial function.
Endothelial cells react to the shear stress caused by blood
ﬂow and produce nitric oxide (NO).3) NO is a vasodepressor
material and stimulates the vessel wall to relax.4) Thisfunction is important for maintaining the homeostasis of thevascular system. The ﬂow-mediated dilation (FMD) method
is used for the conventional evaluation of the endothelial
function.5–7) The FMD method evaluates the endothelial
function by measuring the change in the inner diameter of thebrachial artery after the release of avascularization. However,this method cannot directly evaluate the mechanical properties of the arterial wall.
For a more sensitive and detailed evaluation of theendothelial function and vessel wall mechanical property, amethod of measuring the transient change in viscoelasticity
during FMD was developed by our group.8–12) However, in
this method, stress (blood pressure) and strain (change in
intima-media thickness) are measured in the radial artery in
different arms. Moreover, the change in pulse wave velocity(PWV),13,14) which is the velocity of the pressure wave
caused by the contraction of the heart and propagating
through the blood vessel, due to FMD has not been
considered.15) To solve such a problem, in the present study,
we developed a device for measuring stress and strain in thesame arm. Furthermore, blood pressure waveforms were
measured with two pressure sensors placed along the radial
artery, and the PWV between the sensors was estimated.
Using the estimated PWV, the change in the propagation timedelay of the pulse wave owing to FMD was corrected toobtain better estimates of the viscoelastic constants of theradial arterial wall.
2.

Materials and methods

2.1

Measurement of stress–strain relationshipIn the present study, the radial artery, one of the musculararteries, was measured to obtain the FMD reaction by
applying avascularization using a cuff. It is necessary tomeasure the stress–strain relationship of the arterial wall inorder to estimate viscoelasticity.
For the left radial artery, waveforms of blood pressure were
measured using pressure sensors placed on the skin surface
over the radial artery. The measured waveforms were
calibrated by systolic and diastolic blood pressures measured
with a sphygmomanometer in the right arm. These waveforms of blood pressure were used as the stress acting on thearterial wall.
To determine strain, the minute change in the thickness of
the radial arterial wall during a cardiac cycle was measured
using the phased-tracking method.16) This method canmeasure such minute displacement by calculating the phaseshift due to the change in the propagation time of an
ultrasonic pulse owing to the displacement of a target. To
obtain the change in thickness, the velocities of arterial
wall boundaries [lumen-intima boundary (LIB) and mediaadventitia boundary (MAB)] were estimated. Either velocity
was determined from the phase shift of echoes in two
consecutive frames. The phase shift of echoes was obtainedusing a complex cross-correlation applied to demodulated RF^
signals. From the estimated phase shift ðtÞ,the averagevelocity v^ ðtÞ of the arterial wall at the pulse repetition interval
T was obtained asv^ ðtÞ ¼ ^
c0 ðtÞ
;
2!0 T

ð1Þ

where !0 and c0 are the center angular frequency of the07KF03-1© 2014 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 53, 07KF03 (2014)

M. Sato et al.

pressure
sensor A

pressure
sensor B

ultrasonicprobe

phantom

pulsatile pumpwater tankbase

Fig. 1. (Color online) Illustration of basic experimental system.

ultrasonic pulse and the speed of sound, respectively. The^change in thickness, hðtÞ,between two different depths(LIB and MAB) was obtained from the difference between
the displacements x^ a and x^ b at the LIB and MAB:
^ ¼ x^ a ðtÞ  x^ b ðtÞhðtÞZt¼ ½^va ðtÞ  v^ b ðtÞ dt;
ð2Þ
0

where v^ a and v^ b are the velocities at the LIB and MAB,
respectively.
The phased-tracking method has been used in various
applications, e.g., measurements of the motion and deformation of the arterial and heart walls17–19) for evaluating theviscoelastic properties and the myocardial function,20–23)
and measuring viscoelastic properties with acoustic radiation
force.24,25)
2.2 Correction of change in propagation time delay ofpulse wave

PWV changes with some factors such as the elasticity anddiameter of the artery, and the thickness of the arterial wall.
Because it is difﬁcult to measure ultrasonic RF signals andblood pressure waveforms in the same position, it isnecessary to consider the propagation time delay of pulse
waves. In the present study, blood pressure waveforms were
measured with two pressure sensors placed along the radial
artery to estimate the PWV between sensors. From theestimated PWV, the propagation time of the pulse wave fromthe pressure sensor to the position of the ultrasonic beam wasestimated, and the temporal relationship between stress andstrain was corrected.
The time delay between blood pressure waveforms, xn
and yn , measured by the proximal and distal sensors wasestimated using the cross-correlation function rxy ðmÞ
!
N 1
X
1
rxy ðmÞ ¼
xn ynþm  x y
ð3ÞNx y n¼0
where ðx ; y Þ and ðx; y Þ show the standard deviations andaverages of the blood pressure waveforms, respectively.
When the sampling frequency of the blood pressure waveforms is 10.3 kHz, the resolution in the estimation of timedelay is approximately 0.1 ms.
2.3 Estimation of viscoelasticity from measured stress–
strain relationship

Various models have been used to estimate the viscoelasticityof the blood vessel wall.26–28) Let us assume that theviscoelastic property of the intima-media region of thearterial wall is modeled by the Voigt model.29,30) The most
simple viscoelastic model is the Voigt and Maxwell models.
In the present study, the Voigt model was used because it isassumed that there is no permanent deformation in the arterial
wall. We estimate elasticity and viscosity from the stress–
strain relationship by modeling the stress ^ asZ__
dt þ LPF½ðtÞþ 0 ;
ð4Þ^ ðtÞ ¼ Es LPF½ðtÞ_ Es , ©, 0 , and LPF[0]where ^ ðtÞ is the model of stress, and ,
are the strain rate, static elasticity, viscosity coefﬁcient, bias
stress corresponding to diastolic pressure, and low-pass ﬁlter,
respectively. The viscoelastic constants Es and © and thediastolic blood pressure 0 (minimum blood pressure) are
estimated using the least-squares method by minimizing themean squared difference ¡ between the measured stress ðtÞand the model ^ ðtÞ deﬁned by ¼ Et ½ðtÞ  ^ ðtÞ2 ;ð5Þ

where Et ½ indicates the averaging operation with respect totime for a cardiac cycle.
3.

Basic experiment using phantom

3.1

Experimental method using phantom
In the present study, the feasibility of the proposed method
was validated using a cylindrical phantom made of silicone
rubber containing graphite powder as scatterers (percent
content: 3%). The wall thickness and inner diameter of thephantom were 1 and 8 mm, respectively. We used pulsatile
ﬂow to induce a pulsatile change in internal pressure.
The stress–strain relationship and viscoelasticity of thephantom were measured using the experimental setup
illustrated in Fig. 1. As indicated in Sect. 2.2, blood pressure
waveforms and PWV were measured with two pressure
sensors placed along the radial artery in the in vivo
experiment. Also, in the in vivo measurement, the radial
artery was imaged in a short-axis view for the stablemeasurement of FMD, i.e., an ultrasonic beam could passthrough the central axis of the artery even when the artery
moved during the measurement due to avascularization.
However, the length of the phantom was limited. Therefore,
two pressure sensors (Kyowa PS-1KC) were placed as shown
Fig. 1, and the phantom was imaged in the longitudinal-axis
view to measure vibrations at two points along the phantom

07KF03-2© 2014 The Japan Society of Applied Physics

M. Sato et al.
100

20

30

40

after correction
before correction

50

pressure [mmHg]

10

33.3

90

30.0

80

26.7

70

23.3

60

20.0

50

16.7

40

13.3

30

0

5

0

Fig. 2. (Color online) B-mode image of cylindrical phantom made ofsilicone rubber.

−5

circumferential stress [kPa]

Jpn. J. Appl. Phys. 53, 07KF03 (2014)

10.0−10 −15 −20 −25 −30 −35 −40 −45
change in thickness [µm]
−0.01
−0.02
−0.03
−0.04
strainFig. 3. (Color online) Stress–strain relationships with and without
correction of propagation time delay of pulse wave measured in basic
experiment.

3.2

Results of basic experiment
Figure 2 shows a B-mode image of the anterior wall of thephantom. The change in the thickness of the anterior wallcaused by the change in internal pressure was measured. A
pulsatile change in internal pressure was generated by aﬂow pump. In the basic experiment, the boundaries of thewall, which were tracked by the phased-tracking method,were initially determined automatically by thresholding theecho amplitude. The PWV was estimated using the crosscorrelation function between the velocity waveforms in two
ultrasonic beams. The mean PWV from ﬁve measurements
was 6.95 m/s. The propagation time delay of the pulse wave
from the ultrasonic beam to the pressure sensor was correctedusing the estimated PWV.
Figure 3 shows the measured stress–strain relationshipof the phantom wall with and without correction of the
propagation time delay of the pulse wave.
To evaluate the accuracy of the proposed method, theviscoelastic constants of the phantom were also measured
by a tensile test with a tensile tester (Autograph AG-X,

1000

after correction
before correction

viscosity [kPa s]

800
elasticity [kPa]for the estimation of pulse wave velocity. Blood pressure
waveforms were measured using sensor A and calibratedusing the highest and lowest values obtained by sensor B.
The change in the wall thickness of the phantom wasmeasured using a 22 MHz linear array ultrasonic probe(Diasus Dynamic Imaging). The sampling frequencies of theultrasonic signal and blood pressure waveforms were66.5 MHz and 10.3 kHz, respectively. Using the acquired
ultrasonic signal, vibration velocities at the wall boundaries
were obtained at two points (beams) along the phantom.
By estimating the time delay between the waveforms ofdisplacements measured at these two points, pulse wave
velocity was obtained by dividing the distance between thetwo points (beams) by the estimated time delay. In thisestimation, velocity waveforms were interpolated by a factor
of 63 using reconstructive interpolation31) because of the low
sampling frequency (= frame rate) of velocity waveforms of
320 Hz. We corrected the propagation time delay of the pulse
wave from pressure sensor A relative to the position of theultrasound beam, and the viscoelasticity was estimated fromthe corrected stress–strain relationship.

600
400
200
0

1 2 3 4 5
measurement No.

16
14
12
10
8
6
4
2
0

1 2 3 4 5
measurement No.

Fig. 4. (Color online) Elastic modulus and viscosity constant of phantom
measured by US experiment.

Shimadzu, Japan). The elastic modulus and viscosity constantof the phantom were estimated to be 393 kPa and 42.4 kPa0s,
respectively.
Figure 4 shows the mean and standard deviation of theelasticity and viscosity of the phantom, which were estimatedfrom 20 beams by the proposed method. There was a verysmall change in elastic modulus. Therefore, values with andwithout correction were shown only for viscosity constants.
In the ultrasonic measurement, the means of measured
elasticity and viscosity were 452 kPa (before delay correction: 461 kPa) and 8.0 kPa0s (before delay correction: 6.4
kPa0s), respectively. The correction of the time delay mainly
affects the estimation of viscosity. Elasticity was estimatedwith a mean error of about 50 kPa. The viscosity withcorrection became higher than that without correction andcloser to the result obtained by the tensile test compared withthe ultrasonic measurement with no correction. By correcting
the propagation time delay of PWV, the time delay of strain
from the pressure was increased, as well as the viscosity
constant.
3.3

Discussion of basic experiment
In the basic experiment, the elasticity was estimated with a

07KF03-3© 2014 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 53, 07KF03 (2014)

1000

M. Sato et al.

80
70
viscosity [kPa s]

elasticity [kPa]

800
600
400
200

60
50
40
30
20
10

0

3 4 5 6 7 8
velocity [mm/s].

0

3 4 5 6 7 8
velocity [mm/s]

Fig. 5. (Color online) Elastic modulus and viscosity constant of phantom
measured by tensile test.

small error of about 50 kPa. The viscosity with correction
was closer to the result of the tensile test compared with theultrasonic measurement with no correction. However, theabsolute value of viscosity showed a large error of about
34 kPa0s. The reason for this error is considered to be thedifference between the strain rates in the ultrasonic measurement and tensile test. There is a velocity dependence of theviscoelasticity of real materials. The maximum strain rate of
the phantom was about 0.2 s¹1 in the ultrasonic measurement.
In Fig. 5, the viscoelasticity measured by the tensile tester
was plotted as a function of the velocity of the jig of thetensile tester. The initial gage length was 55.2 mm and, thus,
a jig velocity of about 11 mm/s matched with the strain rateof the ultrasonic measurement. However, only the velocity
range shown in Fig. 5 was available in the tensile tester.
Therefore, we considered the tendency of the relationshipbetween strain rate (jig velocity) and viscosity constant. As
can be seen in Fig. 5, the viscosity constant tends to decrease
with jig velocity, i.e., the viscosity constants estimated byultrasound and tensile test became closer when the strain
rate in the tensile test was closer to that in the ultrasonicmeasurement. Therefore, it was considered that the error in
the estimated viscosity constant was mainly caused by such arate dependence.
4.

Fig. 6. (Color online) Device for in vivo measurement.

130

sensor A
sensor B

Blood pressure [mmHg]

120

110

100

90

80

70

0

0.2

0.4

0.6
0.8
time [s]1

1.2

Fig. 7. (Color online) Blood pressure waveforms obtained by theproximal and distal sensors.

In vivo experiment

4.1

In vivo experiment method
The left radial artery of a healthy male subject (23 years old)
was measured in vivo. In this measurement, ultrasonic RF
echoes (transmit: 22 MHz) were acquired at a sampling
frequency of 66.5 MHz for 2 s and the frame rate was about
320 Hz. To evaluate FMD, the acquisitions were repeatedevery 20 s for 2 min at rest before avascularization and every
about 20 s for 3 min after recirculation. We placed a cuff on
the upper arm or forearm of the subject in order to perform
avascularization to obtain the FMD reaction. Blood pressure
waveforms in the left radial artery were measured with twopressure sensors. To support two pressure sensors and an
ultrasonic probe, we have developed the device shown in
Fig. 6. The waveforms measured by the distal sensor wasused to obtain the stress–strain relationship. Blood pressure
waveforms were acquired at a sampling frequency of
10.3 kHz, together with the acquisition of ultrasonic RF
echoes.

4.2

Results of in vivo experiment
The changes in arterial wall thickness and blood pressure
were obtained for at least one cardiac cycle in eachmeasurement to estimate the viscoelasticity of the radial
arterial wall.
Blood pressure waveforms were measured at two points
along the left radial artery using two pressure sensors. The
distance between the two sensors was 74 mm. Figure 7
shows the measured blood pressure waveforms. We estimatedthe PWV by estimating the time delay using the crosscorrelation function. Figure 8 shows the PWVs estimatedpre- and post-avascularization. The black and blue lines inFig. 8 show transient changes in the PWVs measured in theupper arm and forearm, respectively. Just after avascularization, the pulse wave velocity was very high, it then returns topulse wave velocities similar to those at rest.

07KF03-4© 2014 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 53, 07KF03 (2014)

M. Sato et al.
avascularization(5 min)Pulse wave velocity [m/s]

rest

20

20

15

15

10

10

5

5

0

40
80
time [s]

0

120

0

20

40

60

80
100
time [s]

120

140

160

180

Fig. 8. (Color online) Transient changes in the pulse wave velocities estimated with avascularization in the upper arm (black) and forearm (blue).

140

after correction
before correction

120

viscosity [kPa s]

pressure [mmHg]

130

rest

110
100

20

20

15

15

10

10

5

5

90
0

80
0

−2
−4
−6
change in thickness [µm]

−8

−10

rest

avascularization(5 min)

1200

1200

1000

1000

800

800

600

600

400

400

200

200

0

0 40 80 120
time [s]

0

0

60

120

0

40 80 120time [s]

0

0

60

120

180

time [s]Fig. 11. (Color online) Transient changes in estimated viscosity
constants. Avascularization was applied in the upper arm (black) and forearm(blue).

Fig. 9. (Color online) Measured stress–strain relationships with andwithout correction of propagation time delay of pulse wave.

elasticity [kPa]

avascularization(5 min)180

time [s]Fig. 10. (Color online) Transient changes in estimated static elasticity.
Avascularization was applied in the upper arm (black) and forearm (blue).

Figure 9 shows the measured stress–strain relationships ofthe radial arterial wall with and without correction of the
propagation time delay of the pulse wave. With correction,
the directions of hysteresis loops were corrected fromcounterclockwise to clockwise.
Figure 10 shows the measured transient change in thestatic elasticity owing to FMD. The static elasticity shows anapproximately 40% decrease after avascularization. Although

the FMD reaction was found in both the upper arm and theforearm, the decrease in the elasticity by the avascularization
measured in the upper arm occurred slower and longer thanthat measured in the forearm. In terms of the stability of themeasurement, it is easier to induce avascularization in theupper arm than in the forearm because the upper arm is moredistant from the positions of the ultrasonic probe and pressure
sensors. Figure 11 shows the transient change in viscosity.
The viscosity coefﬁcients measured at rest are almost constant using the proposed correction of the propagation timedelay of pulse waves. Just after recirculation, the viscosity
coefﬁcient became slightly lower than that at rest.
4.3

Discussion of in vivo experiment
In the in vivo measurement, the temporal decrease in thestatic elasticity Es was observed after recirculation. Thisdecrease in static elasticity is considered to be caused by the
FMD reaction. The estimated viscosity was on the orderof that measured in the carotid artery of dogs by in vitro
experiments (5 kPa0s).32) The viscosity coefﬁcients measured
at rest were almost constant, which showed the stablemeasurement achieved by the proposed correction. After
recirculation, the viscosity coefﬁcient became slightly lower
than that at rest.

07KF03-5© 2014 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 53, 07KF03 (2014)

5.

M. Sato et al.

Conclusions

In the present study, we showed that the stress–strain
relationship could be obtained correctly by considering the
propagation time delay of pulse waves. We evaluated theaccuracy of the estimation of viscoelasticity by the proposed
method from a basic experiment using a cylindrical phantom
made of silicone rubber. In the basic experiment, weestimated the viscoelasticity of the phantom by ultrasoundand compared it with that measured by the tensile test. As
a result, a better estimate of viscoelasticity could be obtainedby the proposed method. In addition, in the in vivo
measurement, we applied the proposed method to themeasurement of the viscoelastic properties of the radial
arterial wall by applying avascularization in the upper arm
and forearm. The results show the potential of the proposed
method for the thorough analysis of the transient change inviscoelasticity due to FMD.

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07KF03-6© 2014 The Japan Society of Applied Physics