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Estimation of viscoelasticity of radial artery via simultaneous
measurement of changes in pressure and diameter using a single
ultrasound probe
To cite this article: Takumi Saito et al 2020 Jpn. J. Appl. Phys. 59 SKKE04

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REGULAR PAPER

Japanese Journal of Applied Physics 59, SKKE04 (2020)
https://doi.org/10.35848/1347-4065/ab7f1c

Estimation of viscoelasticity of radial artery via simultaneous measurement ofchanges in pressure and diameter using a single ultrasound probe
Takumi Saito1, Shohei Mori2, Mototaka Arakawa1,2*, Shigeo Ohba2, Kazuto Kobayashi3, and Hiroshi Kanai1,2
1Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan3
Honda Electronics Co. Ltd., Toyohashi 441-3193, Japan2*

E-mail: arakawa@ecei.tohoku.ac.jp

Received December 4, 2019; revised January 21, 2020; accepted March 11, 2020; published online April 1, 2020
To establish an evaluation index for vascular endothelial function, we developed an ultrasonic probe that can measure changes in blood pressure
and blood vessel diameter at the same position in the radial artery. Based on phantom experiments, the pressure waveforms measured
using the piezoelectric effect of the ultrasonic probe element and those using a pressure sensor exhibited a high correlation (correlation coefficient:r = 0.979 – 0.999). We confirmed the continuous measurement of the relationship between changes in blood pressure and the diameter from thein vivo experiments. We could then estimate the changes in viscoelasticity by calibrating the output from the probe element to the absolute bloodpressure values in advance. The average coefficients of variations were 0.02 and 0.24 for elasticity and viscosity, respectively. This study
demonstrated the possibility of measuring changes in the viscoelastic moduli of the radial arterial wall due to flow-mediated dilation using thedeveloped ultrasonic probe. © 2020 The Japan Society of Applied Physics

1. Introduction

Arteriosclerosis is a major cause of cardiovascular diseases.
Several techniques are available for the diagnosis of arteriosclerosis, including intravascular ultrasound and X-ray imaging. However, these techniques are not suitable for repeatedapplications because of their invasiveness. Non-invasive
diagnostic techniques to measure indices such as pulse
wave velocity (PWV)1,2) and ankle-brachial index3) havealso been proposed. However, since these indices arecalculated only as the average value in a wide range ofblood vessels, local changes in the vascular wall characteristics due to the progression of arteriosclerosis cannot bediagnosed. In addition, these parameters are applicable when
the advancement of arteriosclerosis has progressed more thanvascular endothelial dysfunction or changes in smoothmuscle traits. Since vascular endothelial dysfunction andchanges in smooth muscle traits are reversible,4) diagnosis at
an early stage is important. To diagnose arteriosclerosis at an
early stage, it is important to evaluate vascular endothelial
function.
Plethysmography and ﬂow-mediated dilation (FMD) using
ultrasound5–7) are used as the main evaluation methods for
vascular endothelial function. In plethysmography, vascularendothelial function is generally measured by inserting acatheter into the blood vessel to inject vasoactive
substances,8,9) and cannot be applied repeatedly due to its
invasiveness. As a non-invasive technique, plethysmographymeasurements via ischemic reactive hyperemia also has beendeveloped. In this method, instead of injecting vasoactive
substances directly into a blood vessel, an increase in blood
ﬂow after the release of blood is measured. However, it has
not been widely used in clinical practice due to limitations
such as a low speciﬁcity.10) FMD measurement has been
widely recognized for its adoption in the Framingham Heart
Study, and a large volume of clinical data has been
accumulated on its correlation with various risk
factors.11,12) When blood ﬂow increases after the release ofblood, the vasodilator nitric oxide (NO) is produced fromvascular endothelial cells that are stimulated by shear stressfrom the blood ﬂow.13) When NO acts on the medial smoothmuscle, the vascular wall relaxes.14) In an FMD measurement, the ratio of radial artery diameter after restoration andthe resting diameter (%FMD) is calculated. In this case, thearterial diameter is determined by setting the boundary of theblood vessel wall based on ultrasonic A-mode or B-mode
images. However, the distance resolution of the ultrasonicmeasurement is approximately 0.15 mm, even when a
10 MHz high-frequency probe is used. %FMD in healthy
individuals is approximately 6% or more,15,16) and if thevessel diameter is 3 mm, an error of 0.1 mm is equivalent toapproximately 3%, which makes accurate diagnosis difﬁcult.
However, the change in the maximum diameter is indirect,
and is caused by the changes in the mechanical property
associated with the relaxation of the blood vessel wall. If themechanical property can be measured directly, this will prove
to be a better evaluation index. In addition, it was reported
that even when the vascular endothelial function was normal,
the viscoelastic properties of the vascular smooth muscle
changed with organic vascular smooth muscle changes, andthe vasodilator response decreased.17,18) It is important tomeasure the change in the viscoelasticity of the vascular wall
during FMD measurement to distinguish between vascularendothelial dysfunction and organic changes in the vascularsmooth muscle. Therefore, our group focused on changes inthe stress and strain on the blood vessel wall caused byheartbeat.19–22) Signiﬁcant differences were observed in theelastic modulus, rather than the maximum diameter change
after restoration from resting during FMD measurements. We
proposed a new evaluation method for the vascular endothelial function to measure not only elasticity but also viscosity.
However, this method cannot accurately evaluate the viscoelasticity of the vascular wall because the measurement
positions on the blood vessel wall are different for strain
and pressure. Sakai et al. proposed a method to measure
blood pressure and blood vessel diameter at virtually thesame position.23,24) Blood pressure waveforms were thenobtained from the pressure sensors placed on both sides of
the ultrasonic probe, and the delay time from the ultrasonicprobe to the pressure sensors was corrected using the PWV

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calculated from these waveforms. However, it is difﬁcult todetermine the time delay because the PWV changes with achange in blood pressure within a heartbeat. To measure theblood pressure and blood vessel diameter at the same position
by using only an ultrasonic probe, we have demonstrated thatthe blood pressure waveform can be measured via thepiezoelectric effect of the element of the ultrasonicprobe.25) Furthermore, we have developed an ultrasonicprobe that can measure blood pressure and blood vessel
diameter at the same position.26)
In the present study, we ﬁrst veriﬁed the accuracy of theblood pressure waveform measured based on the piezoelectriceffect of the element in an ultrasonic probe. The accuracy was
conﬁrmed using a blood vessel phantom in an aquarium
experiment system. We then measured the blood pressureusing the developed ultrasonic probe on the radial arteryin vivo. Since the blood pressure measured using the ultrasonicprobe element is output as a voltage, the absolute value of thismeasurement must be determined by calibration using thesystolic and diastolic blood pressures obtained using a sphygmomanometer for every beat. To apply this method to the
FMD measurement, it is necessary to perform the calibration
procedure to determine the absolute blood pressure values
using only the ﬁrst beat. Similar to a previous report,27) wecompared the blood pressure waveforms measured using theultrasonic probe element and tonometry, and demonstrated thatthe calibration process to obtain the absolute value of the bloodpressure waveforms was valid for only the ﬁrst beat. In thepresent study, the changes in blood pressure and the diameter
were measured simultaneously by continuously measuring theblood pressure, and the change in viscoelasticity of the bloodvessel wall for each heartbeat was estimated from the relationship between the changes in blood pressure and the diameter.
2. Experimental methods
2.1. Setup of phantom experiment

To conﬁrm the accuracy of the blood pressure waveforms
measured using the ultrasonic probe element, we performed

measurements on a silicone rubber tube that simulated a
blood vessel. Figure 1 shows the experimental system. The
blood vessel phantom was installed in a water tank thatsimulated the circulatory system, and a pulsation pressure
was applied to its lumen using a pulsation pump unit (Tobi,
HTJ-1000). The blood vessel phantom with an inner diameterof 7 mm, a wall thickness of 1 mm, and an Asker C hardnessof 10 was used. The transmural pressure on the phantom walland its waveform were measured using the ultrasonic probe(Honda Electronics), and the internal pressure waveform wasmeasured using a pressure sensor (Kyowa, PS-1KC). To
simulate the structure in which the radial artery is supportedby the radius, a biological tissue phantom with an Asker C
hardness of 15 and a thin plastic plate were placed under the
blood vessel phantom. The ultrasonic probe was directly
pressed against it while the short-axis image of the bloodvessel phantom was observed.
A linear array probe with 192 elements was customized byseparating one center piezoelectric element from the ultrasonic transmitter/receiver unit to measure the blood pressure.
The blood pressure was obtained using the piezoelectriceffect of the ultrasonic probe’s element. The pressure waveform P (t ) measured using the ultrasonic probe element is
described by the following equation in the low-frequency
region.26)
P (t ) =

E
c33
Re33

t

ò0 V (t ) dt,(1 )E
where c33
is the elastic constant under a constant electricﬁeld condition, e33 is the piezoelectric constant, and V (t ) is
the voltage generated in the resistance R. The obtained
output shows the differential of the blood pressure waveform. Therefore, the blood pressure waveform was obtainedby integrating the measured waveform. The output from thepiezoelectric element was passed through an ampliﬁer witha gain of 40 dB and a low-pass ﬁlter (NF, FV-665) with acutoff frequency of 30 Hz, and then output to an oscilloscope.

Fig. 1. (Color online) The experimental setting for the phantom experiment.

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T. Saito et al.

Fig. 2. (Color online) Schematic view of in vivo experiment.

The other 191 elements were used for the ultrasonicmeasurement. The probe was connected to an ultrasounddiagnostic apparatus (Hitachi Aloka, ProSound F75). The
measurement position was set so that the center of the probe
was just above the blood vessel phantom while acquiring the
B-mode image. The output signal acquired from the pressure
sensor was passed through a dynamic strain measuring
instrument (A&D, AS1603) and output to an oscilloscope.
To measure the blood pressure using an ultrasonic probeelement, it is necessary to push down on the blood vessel toﬂatten the upper part. Therefore, we measured pressure
waveforms while changing the force applied to the bloodvessel phantom to investigate the inﬂuence of blood vessel
shape on the blood pressure waveform. We then compared
the pressure waveforms obtained for the ultrasonic probe andthe pressure sensor.
2.2. Experimental setup for in vivo measurements
Figure 2 shows a schematic view of the experimental setting
for in vivo measurements. The blood pressure and bloodvessel diameter were measured at the left radial artery using
the developed ultrasonic probe. The output from the piezoelectric element was passed through an ampliﬁer with a gainof 40 dB, and a low-pass ﬁlter with a cutoff frequency of
30 Hz. The blood pressure waveform was then obtained byintegrating the waveform. By utilizing the B-mode image asshown in Fig. 3, the measurement position was set so that thecenter of the probe was on the center of the radial artery. To
acquire the blood pressure waveform, pushing pressure wasapplied from above the measurement position with theultrasonic probe. The blood vessel diameter was measured
at a center frequency of 7.5 MHz, a sampling frequency of
40 MHz, and a frame rate of 252 Hz. The phased-tracking
method28–31) was used to estimate changes in the diameter.
To obtain the values and waveforms of the blood pressure
continuously, values and waveforms of the blood pressure

were monitored on the right radial artery using tonometry(Nihon Colin, JENTOW-7700). An electrocardiogram (ECG)
was also obtained. The subjects included three healthy males
in their 20 s. Informed consent was obtained from thesubjects and the study was approved by our institutional
ethics committee for human research. All subjects were atleast 2 h after meals and at least 30 min rest before themeasurements. The measurements were performed in asitting position at rest on each subject for 180 s at 60 s
intervals.
Since the measured pressure is output as a voltage as
indicated by Eq. (1), the absolute value was calibrated using
the systolic and diastolic blood pressures obtained via
tonometry. When the blood pressure waveform before
calibration is P (t ), and the systolic and diastolic bloodpressures measured by the tonometry are psys and pdias
respectively, the blood pressure waveform after calibrationPˆ (t ) is given by:psys - pdiasPˆ (t ) ={P (t ) - Pmin} + pdias ,(2 )Pmax - Pmin
where Pmax and Pmin are the maximum and minimum valuesof P (t ), respectively. Calibration to absolute blood pressures
is necessary due to the effects of pressure attenuation in the
subcutaneous tissue and the difference in the position, angle,
and pressing force of the probe element on the radial artery ateach measurement. However, considering the application ofthis method to FMD measurement, it is desirable not tocalibrate to the absolute value at each heartbeat during themeasurement. This is because there is a difference in bloodpressure between the left and right arms after restoration.
Therefore, the absolute value of the blood pressure waveform
measured using the piezoelectric element of the ultrasonicprobe was calibrated using psys and pdias values obtained via
tonometry only for the ﬁrst heartbeat at the start of the

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Fig. 3. (Color online) B-mode image of the left radial artery.

measurement. For subsequent heartbeats, Pˆ (t ) was obtainedby substituting P (t ) for each heartbeat into Eq. (2) using psys ,pdias , Pmax, and Pmin of the ﬁrst beat.
3. Results and discussion
3.1. Phantom experiment

Figure 4 shows the B-mode images of the blood vessel
phantom, pressure waveforms obtained by the ultrasonicprobe and a pressure sensor, and their correlations. From
Figs. 4(a) to 4(c), the force on the blood vessel phantom fromabove by the ultrasonic probe increased. From the B-mode

images, we conﬁrmed that the phantom collapsed as thepushing force increased. Since the measurement positions of
the ultrasonic probe and the pressure sensor were different,
the time for the waveform obtained using the pressure sensor
was adjusted so that the waveform rose with the same timing
to compare the outline of the pressure waveforms to eachother. The shapes of the pressure waveforms that were
measured using the ultrasonic probe and the pressure sensor
were in good agreement with each other and were highly
correlated (correlation coefﬁcient: r = 0.979–0.999). It was
veriﬁed that the pressure waveform can be measured withhigh accuracy using the piezoelectric element of the ultrasonic probe, regardless of the shape of the blood vessel
phantom.
3.2. In vivo experiment
Blood pressure waveforms were acquired using the ultrasonicprobe and tonometry, for 5 consecutive beats for a duration of
180 s at 60 s intervals. Figure 5 shows the blood pressure
waveforms at the start of the measurement and after 180 s.
The delay time of the blood pressure waveform acquired by
the ultrasonic probe caused by passing through a low-passﬁlter was corrected. For the blood pressure waveforms
obtained from the ultrasonic probe element, the absolutevalues were obtained using the systolic and diastolic pressures obtained via tonometry only for the ﬁrst beat, as shown

(a)

(b)

(c)

(a)

(b)

(c)

Fig. 4. (Color online) Results for the phantom experiment for (a) B-mode images of the blood vessel phantom, (b) comparisons of blood pressure waveforms
measured using the ultrasonic probe element and a pressure sensor, and (c) correlations between the two pressure waveforms.

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(a)Fig. 6. (Color online) Temporal changes in systolic and diastolic bloodpressures measured using the ultrasonic probe and a pressure sensor.

(b)

Fig. 5. (Color online) Blood pressure waveforms measured using tonometry and an ultrasonic probe (a) at 0 s (start of measurement) and (b) after
180 s.

in Fig. 5(a), and the relationship was used for the calibrationof all other heartbeats. From Fig. 5(a), we conﬁrmed that the
blood pressure waveforms obtained from tonometry and thepiezoelectric element of the ultrasonic probe were in good
agreement for 5 consecutive heartbeats. In addition, they
were almost identical even after 180 s according to Fig. 5(b).
Figure 6 shows the changes in the systolic and diastolicpressures measured by tonometry and the ultrasonic probe.
Each data point was the average of 5 consecutive beats. The
blood pressure values that were measured using the ultrasonicprobe element were close to those obtained using tonometryfor 180 s. The maximum error of the systolic blood pressure
as measured with the probe element was 3.5%, and that of thediastolic blood pressure was 8.1%. The pressure values
acquired via tonometry were considered to be true readings.
The results suggest that stable measurements were realized
because the position and the pressing force of the ultrasonicprobe strongly affect the blood pressure waveform. By
calibrating the blood pressure readings acquired using thepiezoelectric element of the ultrasonic probe in advance, it
was possible to continuously measure the blood pressure
waveforms over several minutes.

Subsequently, blood pressure waveforms and diameters
were measured using a single ultrasonic probe. Figure 7
shows the relationship between changes in the blood pressure
and the blood vessel diameter obtained for each heartbeat,separated by R-wave timing on the ECG for 3 consecutive
heartbeats measured at 60 s intervals. B-mode images of theradial artery at the time of the R wave are also shown at thetime of each data acquisition. Furthermore, the viscoelastic
moduli were calculated for each beat, and the change overtime is shown in Fig. 8. The viscoelastic moduli were
calculated by applying a least square method using a Voigt
model, which is a basic viscoelastic model for biologicaltissues.32,33)
From the B-mode image and the relationship between thechanges in the blood pressure and the blood vessel diameteras shown in Fig. 7, the position and shape of the blood vessel
did not change signiﬁcantly. As such, the stability of themeasurement was conﬁrmed. For Figs. 7(a) and 7(b), theminimum blood pressure changed approximately 4 mmHg,
the maximum blood pressure changed approximately
5 mmHg, and a maximum deviation of the minimum
diameter was approximately 0.02 mm during 3 heartbeats.
Systolic and diastolic blood pressures are known to ﬂuctuatewith each heartbeat, and we conﬁrmed that they ﬂuctuated byseveral mmHg with each heartbeat by tonometry in Fig. 5.
Therefore, the blood pressure shift in hysteresis is thought tobe caused by normal physiological action, and the bloodvessel diameter shift is caused by the blood pressure change.
From Fig. 8(a), the elastic moduli estimation results showed
little variation between heartbeats, and the average coefﬁcientof variations (CV) between heartbeats was 0.02. The results
also showed little variation over time, and the CV of theaverage value between time points was 0.06. These results
demonstrated that we can measure changes in the elastic
moduli of the blood vessel wall for at least 180 s. For theviscosity results shown in Fig. 8(b), the average CV between
heartbeats was 0.24, and the CV of the average value
between time points was 0.24. The variations in viscosity
were larger than the variations in elasticity. The elastic
modulus is related to strain, whereas the viscosity is related tothe strain rate. Thus, it is likely to be affected by physiologicalaction and slight body movements. The hysteresises shifted for
3 consecutive heartbeats in Figs. 7(a) and 7(b), and they were

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T. Saito et al.

(a)

(b)

(c)

(d)

Fig. 7. (Color online) Relationship between changes in the blood pressure and the diameter of the blood vessel in B-mode images for 3 consecutive
heartbeats (ﬁrst, second, and third shown in ﬁgure) (a) at 0 s (start of measurement), (b) after 60 s, (c) after 120 s, and (d) after 180 s.

little change in Figs. 7(c) and 7(d). However, in Fig. 8, evenwhen comparing the viscoelastic moduli at the times for
Figs. 7(a)–7(d), the variations in 3 heartbeats were almost thesame. This is because the slope of the hysteresis related tothe elasticity and the area of the hysteresis related to theviscosity hardly changed. Therefore, it is considered that thesechanges among heartbeats have little effect on the estimatedviscoelasticity.
Figure 9 shows the viscoelasticity estimation results for thethree subjects. For all the subjects, the elasticity and viscosity
were of the same order. Based on the results for the subjects,
a relationship was not observed between the elasticity and theviscosity. Although the viscoelastic moduli that were estimated even at rest exhibited variations, it is considered to bewithin an appropriate range compared to the variations of theviscoelastic parameters at rest, in the experiments by Sakai
et al.24) and Kutluk et al.34) In the experiment by Learoyd,35)
the elastic modulus of the carotid artery of young subjects
was approximately 100–500 kPa in 50–130 mmHg, and theelasticity in Fig. 9(a) was smaller. This is because the radial
artery, which is a blood vessel thinner than the carotid artery,is the target, and the blood vessel has an elliptical-cylinder
shape because of the deformation of the blood vessel during
measurement. When a blood vessel is elliptical, the diameterin the ultrasonic beam direction becomes smaller, and it iseasy for the vessel to spread in that direction. As a result, theelastic moduli were estimated to be small. To address thisproblem, it is necessary to construct a viscoelastic model
considering the shape of the blood vessel.

4. Conclusions

In the present study, we compared the pressure waveforms
measured using an ultrasonic probe element and a pressure
sensor for a blood vessel phantom, in the ﬁrst instance. It was
conﬁrmed that the pressure can be measured with highaccuracy regardless of the shape of the blood vessel phantom
using the ultrasonic probe element.
Subsequently, it was shown that the blood pressure waveforms and blood pressure values can be continuously measured
for several minutes by calibrating the output from the probeelement to the absolute blood pressure values in advance. In
addition, the blood pressure and the changes in the blood vessel
diameter were measured simultaneously. In addition, theviscoelastic moduli of the radial arterial wall for each heartbeat
were estimated based on the relationship between them. Similar
experiments were conducted for the three subjects.
From these results, it was determined that we cancontinually measure the relationship between changes inthe blood pressure and the blood vessel diameter to estimatechanges in viscoelasticity using a single ultrasonic probe. To
perform this measurement, it is necessary to calibrate theoutput from the probe element to the absolute blood pressure
values at the start of measurements. This study demonstrates
the possibility of measuring changes in the viscoelastic
moduli on the radial arterial wall during FMD measurement
using the developed ultrasonic probe.
In the future, by applying this method to FMD measurement, we intend to measure the temporal changes of the

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viscoelastic moduli of the blood vessel wall, and to evaluate
vascular endothelial function.
Acknowledgments
(a)

(b)

Fig. 8. (Color online) Temporal changes and their average over 3
consecutive heartbeats, (a) elasticity and (b) viscosity.

(a)

(b)

Fig. 9. (Color online) Temporal changes and their average over 3
consecutive heartbeats for 3 subjects, (a) elasticity and (b) viscosity.

This work was partially supported by JSPS KAKENHI
19K22943.

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