REGULAR PAPER

Japanese Journal of Applied Physics 55, 07KF11 (2016)
http://doi.org/10.7567/JJAP.55.07KF11

Accurate evaluation of viscoelasticity of radial artery wall during
ﬂow-mediated dilation in ultrasound measurement
Yasumasa Sakai1, Hirofumi Taki2,1, and Hiroshi Kanai1,2*
1Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan2*E-mail: kanai@ecei.tohoku.ac.jp
Received November 13, 2015; accepted March 25, 2016; published online June 16, 2016
In our previous study, the viscoelasticity of the radial artery wall was estimated to diagnose endothelial dysfunction using a high-frequency(22 MHz) ultrasound device. In the present study, we employed a commercial ultrasound device (7.5 MHz) and estimated the viscoelasticity usingarterial pressure and diameter, both of which were measured at the same position. In a phantom experiment, the proposed method successfully
estimated the elasticity and viscosity of the phantom with errors of 1.8 and 30.3%, respectively. In an in vivo measurement, the transient change inthe viscoelasticity was measured for three healthy subjects during ﬂow-mediated dilation (FMD). The proposed method revealed the softening of
the arterial wall originating from the FMD reaction within 100 s after avascularization. These results indicate the high performance of the proposed
method in evaluating vascular endothelial function just after avascularization, where the function is difﬁcult to be estimated by a conventional FMD
measurement. © 2016 The Japan Society of Applied Physics

1.

Introduction

Cardiovascular disease is a major cause of death in Japan,
and atherosclerosis is one of the main causes of cardiovascular disease. As a method for the diagnosis of atherosclerosis, there are several techniques such as intravascularultrasound and diagnosis by X-ray imaging. However, thesetechniques are unsuitable for repeated tests because of theirinvasiveness and radiation exposure. As noninvasive diagnostic methods for atherosclerosis, Wetter and Kenner1) and
McDonald2) proposed an index of pulse wave velocity(PWV), and Weitz et al.3) proposed an ankle brachial index(ABI). However, these indices are intended to diagnose
advanced lesions, not those prior to vascular endothelial
dysfunction. In an early stage of atherosclerosis, it isconsidered that vascular endothelial function is reduced
before the appearance of plaques and that the reduction of theendothelial function should still be reversible.4,5) Therefore,
for the early diagnosis and treatment of atherosclerosis, it isimportant to develop a noninvasive diagnostic method toevaluate vascular endothelial function.
Endothelial cells react to the shear stress caused by blood
ﬂow and produce nitric oxide (NO),6) which is a vasodepressor material that stimulates the vessel wall to relax.7)
This function is important for maintaining the homeostasisof the vascular system. For the evaluation of vascularendothelial function, there is a conventional technique formeasuring the transient change in the inner diameter of thebrachial artery caused by ﬂow-mediated dilation (FMD) after
the release of avascularization.8–10) However, this method
cannot be used to directly evaluate the mechanical properties(viscoelasticity) of the radial artery wall and it is diﬃcult todiagnose the endothelial function because the rate of diameterchange is low, at most about 6% in healthy subjects.11,12)
For a more accurate evaluation of the endothelial function,
our group has focused on the fact that the change in diameter
depends on the mechanical properties of the vessel, and wehave measured the transient change in viscoelasticity during
FMD with respect to arterial pressure and wall thickness atthe same position.13–18) However, the viscoelasticity estimated by the employed method had a large variance because

it is diﬃcult to measure the minute change in thickness of theradial artery wall, i.e., several micrometers. Furthermore, themethod employed a high-frequency (22 MHz) ultrasounddevice with a single beam, which was much diﬀerent from acommercial ultrasound diagnostic apparatus. To solve these
problems, in the present study, we employed a commercial
ultrasound device with a center frequency of 7.5 MHz andmeasured the change in the diameter of a radial artery, about
100 µm, from which the viscoelasticity of the radial arterywall was estimated. Moreover, in order to measure thechanges in the diameter and pressure of the radial artery at
the same position, two pressure sensors were employed tocorrect the time delay due to the pulse wave propagation.
After evaluating the accuracy of the proposed method in theestimation of the incremental viscoelasticity of a silicone tube
phantom, the proposed method was applied to three healthy
subjects to measure the changes in diameter and viscoelasticity during FMD.
2.

Methods

2.1

Measurement of arterial pressure and diameter
For the noninvasive evaluation of the elasticity of the artery orsoft tissue, some methods have been developed recently.19,20)
On the other hand, for the noninvasive characterization ofviscoelasticity, there have been several methods based on thehysteresis property between the force and the displacement,21)
and based on the dispersion of shear wave propagation
velocity.22) In the present study, for the measurement ofviscoelasticity in the radial artery wall, changes in thickness
and pressure were simultaneously measured. In our previous
study, the change in thickness was measured using highfrequency ultrasound transmission with a center frequency of
22 MHz. However, when using a commercial transcutaneous
ultrasound device with a center frequency of 7.5 MHz, it wasdiﬃcult to accurately measure the change in the thickness of
the radial artery wall. Alternatively, the change in the diameterof the radial artery was measured to estimate the viscoelasticity of the radial artery.
For the measurement of the pressure at the same point asthat for the change in diameter using ultrasound, as shown in
Fig. 1, the arterial blood pressure waveforms pA(t) and pB(t)07KF11-1© 2016 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 55, 07KF11 (2016)

Y. Sakai et al.

!
"
!^
:
pd
1 ðtÞ ¼ pB t $2

Fig. 1. (Color online) Device for in vivo measurement of viscoelasticity
for the radial artery.

Fig. 2. (Color online) Blood pressures measured by two pressure sensors.
The correlation window was set between the two dotted lines.

at two points on the left radial artery were simultaneously
measured using two pressure sensors. The time delay τ frompA(t) to pB(t) was determined by maximizing the crosscorrelation function23) as!^ ¼ arg max rAB ð!Þ;
ð1Þ
!
"
#
N$1
X
1
rAB ð!Þ ¼
ðpA ðn!tÞ $ pA ÞðpB ðn!t þ !Þ $ pB Þ ;N"A "B n¼0

ð2Þ
where ð"A ; "B Þ and ðpA ; pB Þ show the standard deviations andaverages of blood pressure waveforms, respectively. As
shown in Fig. 2, the window of cross-correlation function
was set from the onset of the rise of blood pressure to thepeak time of its waveform in order to eliminate the eﬀect of
the reﬂection from the vascular periphery.
In the present study, we assume that the PWV and thepressure waveform between two pressure sensors areconstant. Under this condition, the pressure waveform p1(t)at the position of the ultrasound probe located at the center of
two pressure sensors was estimated by compensation for thedelay time from the position of the ultrasound probe to that ofthe pressure sensor B:

ð3Þ

Therefore, the pressure p1(t) could be measured at the same
position as that for the measurement of diameter D(t) by theultrasound probe.
The pressure measured by the pressure sensor reﬂects the
blood pressure in the radial artery. We assume that the
maximum and minimum blood pressures in the left radial
artery are the same as those in the right radial artery. The
blood pressure in the right radial artery was measured using a
sphygmomanometer, which was employed to calibrate thepressure waveform measured by the pressure sensor on theleft radial artery.
The arterial diameter during a heartbeat was measured
using a 7.5 MHz ultrasound probe. The change in arterial
diameter was calculated by applying the phased-tracking
method24–27) to the receive RF signals. By this method, aminute displacement is estimated by calculating the phaseshift due to the displacement of a target as follows. The
received ultrasound pulse has a phase delay, θ(t), corresponding to the path length. The phase shift, Δθ(t) =θ(t + T) − θ(t), is estimated from two consecutive echoes.
From the phase shift, the velocity of the target at the time
t + T=2 is given by!
"T
c !#ðtÞ
v tþ
;
ð4Þ
¼$
2
2!0 T
where T is the pulse repetition interval, and ω0 and c are thecentral angular frequency of the ultrasound wave and the
speed of sound, respectively. The speed of sound in the tissue
is assumed to be 1,540 m=s. The change in diameter, D(t), is
obtained by the integration of the diﬀerence between thevelocity waveforms for the anterior and posterior walls.

2.2

Viscoelasticity estimation
By assuming that the viscoelasticity of the artery wall follows
the Voigt model,28) we estimate the stiﬀness parameter β
and viscosity parameter η from the following equation of
the pulse pressure with respect to arterial pressure anddiameter:29)
"
#
pd
d
1 ðtÞ
ln
ð5Þ
¼ $"1 ðtÞ þ % "1 ðtÞ;pmin
dt

where pd
1 ðtÞ is the modeled blood pressure and ε1(t) denotes
the strain of the diameter. The unit of the viscosity parameterη is second. The viscoelastic constants β and η are estimatedby applying the least-squares method to minimize thediﬀerence between the measured and modeled arterialpressure waveforms as2& ¼ Et ½j ln p1 ðtÞ $ ln pd
1 ðtÞj ';ð6Þ

where Et[·] denotes the averaging operation with respect totime during a single heartbeat. To suppress noise components, we examined the spatially averaged arterial diameterand viscoelasticity by setting three beams around the centerof the radial artery.
2.3

Experimental setting in the phantom experiment
In the present study, the feasibility of the proposed method
was validated using a cylindrical phantom made of silicone

07KF11-2© 2016 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 55, 07KF11 (2016)

Y. Sakai et al.

Fig. 3. (Color online) Basic experimental system.

rubber that contained graphite powder as scatterers. Pulsatile
ﬂow was used to induce a pulsatile change in internalpressure. Incremental viscoelasticity was estimated from therelationship between pressure and diameter shown by
Dmin bd
P2 ðtÞ ¼ Einc "2 ðtÞ þ %inc "2 ðtÞ;dt
2hFig. 4. B-mode image of silicone tube.

ð7Þ

where Pb2 ðtÞ is the model pulse pressure, and ε2, Einc, ηinc, andh are the strain of diameter, incremental elasticity, incremental viscosity, and wall thickness, respectively. The unit of
the incremental viscosity ηinc is Pascal-second. The incremental viscoelasticity (Einc and ηinc) was estimated by theleast-squares method with the minimization of the meansquared diﬀerence.
Internal pressure waveforms and PWV were measured
with two pressure sensors (Kyowa PS-1KC) located 50 mm
apart, as shown in Fig. 3. In the in vivo experiment, thepressure waveforms measured using pressure sensors A and
B were calibrated by the direct measurement of the waterpressure using sensor C. The change in the inner diameter ofthe phantom was measured using an ultrasound diagnostic
device (Hitachi-Aloka ProSound F75) with a 7.5 MHz linear
array probe (Hitachi-Aloka UST-5415) placed at the center of
the two pressure sensors. The sampling frequency of theultrasound signal was 40.0 MHz and the frame rate was
252 Hz. Furthermore, the propagation time between thepressure waveforms measured by sensors A and B was
estimated by using the cross-correlation function, andPWV was estimated from the relationship between distanceand propagation time. Finally, as shown in Eq. (2), thepropagation time from the pressure sensor to the ultrasoundprobe was corrected using this PWV.
2.4

Experimental setting in vivo
In this study, the left radial arteries of three healthy subjects(22–23 years old) were measured. In the in vivo experiment,
the same ultrasound-data acquisition setting as that in thephantom study was used, the two pressure sensors being
located 74 mm apart. Blood pressure waveforms wereacquired at the sampling frequency of 1.0 Hz in the left radial
artery. In addition, the blood pressure waveforms were
calibrated by systolic and diastolic blood pressures measured
with a sphygmomanometer in the right radial artery 5 minafter recirculation, because there should have been a small
diﬀerence between the right and left arterial pressures at thetime. The transient changes in diameter and viscoelasticity

Fig. 5. (Color online) Relationships between diameter and pressure
before and after correction of the propagation time.

during FMD were measured. This measurement was repeatedevery 20 s for 3 min at rest before avascularization and about
every 10 s for 5 min after recirculation. Although somemethods have been proposed to automatically determine theboundaries of the arterial wall from the received RF signals,30)
in the present study, the lumen-intima boundaries for theanterior and posterior walls were determined from the local
maxima of the envelope signal of the received RF signal.
3.

Results

3.1 Results of the basic experiment using vessel
phantom

Figure 4 shows a B-mode image of the vessel phantom. The
PWV from pressure sensors A to B was estimated. The mean
PWV using four measurements was 1.83 m=s, and the
propagation time delay between pressure sensor A and theultrasound probe was corrected using the estimated PWV.
Figure 5 shows the relationships between the diameter of thephantom and the pressure before and after the correction of
the propagation time delay of the pulse wave.
Figure 6 shows the mean and standard deviation of theincremental viscoelasticity by using three beams near thecenter of the phantom tube in four measurements. In the07KF11-3© 2016 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 55, 07KF11 (2016)

Y. Sakai et al.

Fig. 6. (Color online) Measured viscoelasticity of phantom in basic experiment using phantom.

Fig. 7. (Color online) Transient changes in systolic (solid lines, ps) and diastolic (dot lines, pd ) blood pressures during FMD for three healthy subjects.

ultrasound measurement, the measured mean incremental
elasticity and viscosity were 376.5 kPa and 21.1 kPa·s,
respectively. The deviations of elasticity and viscosity are
22.6 kPa and 1.3 kPa·s, respectively. This shows that the
proposed method had a variance smaller than that of ourprevious study, where the deviations of elasticity andviscosity were about 130.0 kPa and 2.3 kPa·s, respectively.
To evaluate the accuracy of the proposed method, theviscoelasticity of the phantom was also measured using atensile tester (Shimadzu Autograph AG-X). The estimatedelastic and viscosity moduli of the phantom were 383.5 kPa
and 27.5 kPa·s, respectively. Thus, the estimation errors of
the elasticity and viscosity were 1.9 and 30.3%, respectively.
3.2

Results of the in vivo experiment

Figure 7 shows the transient changes in systolic and diastolicblood pressures during FMD. The pulse pressure estimatedby the proposed method largely decreased just after
avascularization.
Figure 8 shows the relationships between diameter andpressure in the radial artery before and after correction using
the propagation time and the estimated hysteresis loop using
the Voigt model. The hysteresis loop depicted using theestimated parameters was close to that obtained after
correction using the propagation time, which shows theeﬀectiveness of the proposed method.
Figure 9 shows the transient change in the arterial diametermeasured during FMD in three subjects. In all subjects, thediameter increased more than 10% after avascularization.

Fig. 8. (Color online) Measured hysteresis loops before and after
correction of the propagation time and estimated hysteresis loop in in vivo
measurement.

Because the increase in the diameter of healthy people ismore than 6%, this result is consistent with previous reports.
Figures 10 and 11 respectively show the transient changes
in the estimated stiﬀness parameter β and viscosity parameterof the radial artery wall during FMD reaction. In all threesubjects, the stiﬀness parameter β temporarily decreased after
avascularization. The variance of the viscosity parameter
was smaller than that in the previous study,18) showing therobustness of the proposed compensation method. The small
variance may be due to the estimation of arterial diametercompared with that of artery wall thickness.

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Y. Sakai et al.

Fig. 9. (Color online) Transient change in the diameter during FMD for three healthy subjects (circles: the time showing the maximum diameter).

Fig. 10. (Color online) Transient change in the stiﬀness parameter β during FMD reaction for 3 healthy subjects (dotted lines: the mean during rest, circles:
the time showing the smallest stiﬀness parameter).

Fig. 11. (Color online) Transient change in the viscosity parameter during FMD reaction for 3 healthy subjects (dotted lines: the mean during rest, circles:
the time showing the smallest viscosity parameter).

Figure 12 shows the measured relationship between
diameter and pressure during the FMD reaction for subject
A. The slope of the hysteresis loop, which corresponds to thestiﬀness parameter β, decreased after avascularization. These
results validate the accuracy of the proposed method.
4.

Discussion

In the experiment using a phantom, the incremental elasticity
estimated by the proposed method was close to that measured
by a tensile tester, the diﬀerence being about 1.9% of thevalue estimated by the proposed method. However, thediﬀerence in incremental viscosity was 30.3%. This large
diﬀerence may have been caused by the diﬀerence in strain
rate between the experiment using the proposed method andthe tensile test. Because the viscosity is generally largely
dependent on the strain rate, it is necessary to use the samestrain rate in order to evaluate the estimation accuracy of theviscosity. The maximum strain rate of the phantom was about
0.18%=s in the ultrasound measurement. However, the upper
limit of the strain rate was 0.15%=s in the tensile test, and it

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Y. Sakai et al.

a phantom experiment. The obtained results showed theaccuracy of the reproducibility of the proposed method. In
addition, arterial diameters and viscoelasticity during FMD
reaction were measured in three healthy subjects. The
proposed method revealed the softening of the arterial wall
due to the FMD reaction within 100 s after avascularization.
This result indicates the high performance of the proposed
method in evaluating vascular endothelial function just after
avascularization, where the function is diﬃcult to be estimated by a conventional FMD measurement.

Fig. 12. (Color online) Measured relationship between diameter andpressure during FMD for subject A.

was not possible to use the same strain rate for bothmeasurements.
The pulse pressure estimated by the proposed method
largely decreased just after avascularization, as shown in
Fig. 7. The decrease in arterial blood pressure may havebeen caused by the stoppage of blood circulation, because
blood circulation maintains the diﬀerence between arterial
and venous blood pressures. During avascularization, arterial
blood pressure decreases and venous blood pressure
increases. Since the arterial blood pressure did not recover
immediately, this may have caused the low pulse pressure
just after avascularization.
Within 50 s after avascularization, the arterial wall
softened; however, the arterial diameter was not large enoughcompared with that at rest because of the low systolic bloodpressure, as shown in Figs. 7, 9, and 10. From 50 to 150 s
after avascularization, the arterial diameter increased as thesystolic blood pressure increased, and the diameter had the
maximum value from 100 to 150 s after avascularization.
This result indicates that a conventional FMD measurement
does not consider the decrease in systolic blood pressure, andthe conventional measurement will work from 50 to 150 s
after avascularization, that is, after the recovery of systolicblood pressure.
The proposed method considers the decrease in systolicblood pressure in estimating the stiﬀness parameter β. As
shown in Fig. 10, within 100 s after avascularization, thestiﬀness parameter β estimated by the proposed method
decreased, that is, the arterial wall softened by the FMD
reaction. This result indicates the high performance of the
proposed method in evaluating vascular endothelial function
just after avascularization, where the function is diﬃcult to be
estimated by a conventional FMD measurement.
5.

Conclusions

In the present study, we proposed a method of estimating
viscoelasticity that uses two pressure sensors for arterialpressure measurement and a commercial ultrasound diagnostic device with a 7.5 MHz probe for arterial diametermeasurement at the same position. We evaluated the accuracyof the estimation of viscoelasticity by the proposed method in

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