Japanese Journal of Applied
Physics

BRIEF NOTE

Estimation of viscoelasticity of radial artery during flow-mediateddilatation using a single ultrasound probe based on blood pressure
measurement via pulse transit time method
To cite this article: Yuto Shoji et al 2021 Jpn. J. Appl. Phys. 60 SDDE03

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BRIEF NOTEJapanese Journal of Applied Physics 60, SDDE03 (2021)
https://doi.org/10.35848/1347-4065/abef0b

Estimation of viscoelasticity of radial artery during flow-mediated dilatation using
a single ultrasound probe based on blood pressure measurement via pulse transit
time method
Yuto Shoji1, Shohei Mori2, Mototaka Arakawa1,2*, Shigeo Ohba2, Kazuto Kobayashi3, and Hiroshi Kanai1,2
1Graduated School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan
Graduated School of Engineering, Tohoku University, Sendai 987-8579, Japan3
Honda Electronics Co. Ltd., Toyohashi 441-3193, Japan2*

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

Received December 2, 2020; revised February 6, 2021; accepted March 16, 2021; published online March 31, 2021
We developed a single ultrasound probe to simultaneously measure blood pressure and changes in the diameter of the radial artery to estimate thewall viscoelasticity during flow-mediated dilatation (FMD). This probe can be used for the early diagnosis of arteriosclerosis. This paper introduces
the pulse transit time method to accurately measure changes in blood pressure during FMD. Using the single ultrasound probe and the proposed
method, in vivo experiments involving three subjects were conducted, and reasonable results on blood pressure were obtained. Thus, theusefulness of the pulse transit time method was experimentally confirmed. © 2021 The Japan Society of Applied Physics

Vascular endothelial dysfunction occurs during the earlystages of arteriosclerosis. As the dysfunction can be treatedthrough medication and relevant lifestyle modiﬁcation,1) an
evaluation of the vascular endothelial function is important
for the early diagnosis and treatment of arteriosclerosis. To
assess the vascular endothelial function, several methods
have been clinically employed including invasiveplethysmography2,3) and non-invasive plethysmography,4)which use ischemic reactive hyperemia and ﬂow-mediateddilatation (FMD) test.5–7) Among them, the FMD test is
widely used clinically because it is simple andnon-invasive.8,9) However, it does not directly evaluate themechanical properties of the vessels, as it only measures therate of vasodilatation as an indicator. During FMD, the shear
stress in a vessel increases owing to the rapid increase inblood ﬂow after avascularization, and nitride oxide (NO) is
secreted by the vascular endothelial cells. NO acts on thesmooth muscle in tunica media causing the vessel wall torelax and vessel diameter to dilate.10,11) In other words,
vascular dilation is caused by changes in the mechanicalproperties of the vessel wall. Therefore, elasticity measurement during FMD is a direct evaluation of the vascularendothelial function.
We developed a single ultrasound probe that simultaneously measures vessel diameter and blood pressure waveforms at the same position to precisely determine theviscoelastic properties of the vessel wall.12) The developed
probe detects blood pressure waveforms by separating acentral element from the conventional ultrasound probe andusing it as a piezoelectric sensor. Because the pressure
waveform is measured as a voltage value, it is necessary tocalibrate it to the blood pressure. Moreover, determining thechange in viscoelasticity during FMD requires measuring theblood pressure over time. However, it is difﬁcult to measure
blood pressure using a cuff for calibration during FMD. We
have conﬁrmed that viscoelastic properties are measured withhigh accuracy by calibrating the blood pressure waveform atrest.13) However, accurate blood pressure measurement is
difﬁcult in this procedure because the acquired voltage isaffected by the change in the pushing pressure of theultrasonic probe to the blood vessel caused by the unintended
body movement during the FMD measurement.14)

In this study, ﬂuctuations in viscoelastic properties during
FMD were experimentally corrected by introducing the pulse
transit time (PTT) method to determine the systolic anddiastolic blood pressures, regardless of the absolute value ofthe voltage acquired by the probe.15) Because the PTT
method estimates the blood pressure values using only
PTT, it is possible to calibrate the blood pressure waveform
during FMD without using a cuff.
Because the blood pressure waveform measured by thedeveloped ultrasound probe is output as voltage, the waveform should be calibrated at each heartbeat, as previously
mentioned. The blood pressure value after calibration p (t ) is
given bypsys - pdias
p (t ) ={p (t ) - pmin} + pdias ,(1 )pmax - pmin
where pmax and pmin are the maximum and minimum valuesof p (t ), respectively, and psys and pdias are the systolic anddiastolic blood pressures, respectively. pmax , pmin , and p (t )were obtained as voltage values.
In conventional methods,13,14) systolic and diastolic bloodpressures measured using a sphygmomanometer at rest wereused as psys and pdias in Eq. (1), respectively, whereas in thisstudy, those determined by the PTT method were used toaccurately reﬂect the changes in blood pressure during FMD.
Blood pressure measurement using PTT is a reliable method
currently being studied for cuff-less blood pressure
measurements.16–18) The method can determine the bloodpressure using only the transit time of the blood pressure
pulse wave, as described below.
Using the Moens−Korteweg equation,19) the pulse wave
velocity PWV is described by the elastic modulus E of theartery as
PWV =

d
=
TPT

Eh
,
2rr

(2 )

where TPT is the transit time of the blood pressure between
distance d from the heart to the artery, h is the thickness ofthe vessel wall, ρ is the density of the blood, and r is theradius of the vessel. An exponential relationship between thevascular modulus E and mean blood pressure is given by20)

SDDE03-1© 2021 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 60, SDDE03 (2021)

Y. Shoji et al.

E = E 0 e aP ,(3 )where E0 is an intercept, α is a constant speciﬁc to eachmeasurement object, which can be approximated by aconstant for the parent population, and P is the mean bloodpressure within a heartbeat.20) From Eqs. (2) and (3), themean blood pressure P (T ) of an arbitrary heartbeat T is givenby
P (T ) =1
2rrd 22ln
ln TPT.
a
a
E0 h

(4 )

The changes in PTT signiﬁcantly affect changes in bloodpressure when compared to those in other coefﬁcients from
Eq. (4). Here, by assuming that E0, h , r, r , and d remainunchanged during the period from the reference heartbeat T0
to the heartbeat T, the mean blood pressure P (T0 ) in Eq. (4)holds for T0, and the change in the mean blood pressure DP isgiven by the ratio of TPT to TPT0 as
DP = P (T ) - P (T0) =

TPT0
2
ln
,
a
TPT

(5 )

which shows that the change in DP depends only on thepulse transit time of the blood pressure.
The elasticity Eq of the wall circumference direction can bedeﬁned as
psys - pdias
,
(6 )
Eq =
2p (rsys - rdias ) / 2prdias
where rsys and rdias are the radii during systole and diastole,
respectively. Equation (6) holds for heartbeats T and T0. By
substituting E of Eq. (2) with Eq of Eq. (6), we obtain2
2
TPT( psys - pdias ) = TPT( psys0 - pdias 0 ) ,0(7 )where psys0 and pdias0 are the systolic and diastolic pressures,
respectively, for the reference heartbeat T0. From Eq. (7), psys
is determined as
psys = pdias + ( psys 0 - pdias 0 )

2
TPT
0
2
TPT

.

(8 )

By substituting the relation P (t ) = ( psys + 2pdias ) /3 and psysof Eq. (8) in Eq. (5), pdias is determined as
pdias =

psys 03+-2pdias 0+

2 ⎛ TPT0 ⎞ln ⎜⎟a ⎝ TPT ⎠32
psys0 - pdias 0 TPT
0
3

2
TPT

(9 )

was ﬁtted to the Voigt model to estimate the viscoelasticity ofthe vessel wall.
We measured the blood pressure p (t ) and vessel diameter2r (t ) for three healthy men in their 20 s during FMD in theradial artery, and estimated changes in the elasticity E (t ) andviscosity h (t ) of the radial arterial wall. The experimental
system and protocol were the same as those described inRef. 14. Informed consent was obtained from all subjects,
and the study was approved by our institutional ethics
committee for human research.
Figures 1−3 show the measurement results of PTT,
systolic (solid line) and diastolic (dashed line) blood pressures, and estimates of the elastic modulus E (t ) (solid line)
and viscosity h (t ) (dashed line), respectively. Further, theresults for subjects A−C are shown with red, blue, and green
lines, respectively, and ﬁgures (a) and (b) show the results
obtained at rest and after recirculation, respectively.
Figure 1 shows that the PTT immediately increased afterrecirculation in all subjects and gradually approached theresting values, which correspond to the decrease in elasticity
after recirculation in the FMD. This result reﬂects thedecrease in the elasticity due to the FMD because the pulse
transit time TPT increases as the elasticity E decreases, as
given by Eq. (2).
Figure 2 shows that psys and pdias decreased after recirculation and gradually increased to near-resting values for all
subjects. The results are reasonable because the bloodpressure, which decreased immediately after recirculation,
was lower than that at rest because of vasodilatation owing to
FMD. This trend was not observed through the conventional
method,14) thus indicating the effectiveness of the proposed
method.
In Fig. 3, although the magnitude of elasticities differedfrom the three subjects, they at rest were of the same order ofmagnitude. However, the elasticity, which changed afterrecirculation, showed a different trend among the subjects,
although the trends of the blood pressure change weresimilar. This might be because the vessel was deformed
such that the upper part of the vessel was ﬂattened for themeasurement of the blood pressure waveform using theultrasound probe. If the shape of the artery changed during
the measurement, the estimated viscoelasticity was affectedeven when the actual mechanical properties did not change.
This is because the viscoelastic property was estimated fromthe relationship between the applied blood pressure and
(a)

(b)

.

In this study, the pulse transit time TPT was obtained as thetime difference from the R wave of the electrocardiogram tothe peak of the blood pressure waveform in the same cardiac
cycle. Thus, systolic blood pressure psys and diastolic bloodpressure pdias can be determined without relying on the output
voltage obtained from the ultrasound probe because they are
determined using only TPT, systolic blood pressure psys0, anddiastolic blood pressure pdias0 at the reference heartbeat T0.
The change in the vascular diameter 2r (t ) was measured
using the phased-tracking method,21) and the relationshipbetween the blood pressure p (t ) and vascular diameter 2r (t )Fig. 1. (Color online) Pulse transit time during the FMD measurement(a) at rest, (b) after the recirculation.

SDDE03-2© 2021 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 60, SDDE03 (2021)(a)Y. Shoji et al.

(b)

Fig. 2. (Color online) Systolic (solid line) and diastolic (dashed line) bloodpressure during the FMD measurement (a) at rest, (b) after recirculation.

(a)

(b)

return to its original value for each heartbeat. Therefore, morestable measurement of the vessel diameters is required toobtain more accurate viscosity.
In this study, we showed that the PTT method is useful formeasuring blood pressure because the measurement values
do not depend on the pressure applied by the ultrasoundprobe. The measured blood pressure changes showed asimilar trend in all the subjects. The results reﬂect the change
in the elastic modulus during the FMD. However, Eq. (2)suggests that the PTT may change depending on the vessel
diameter. Therefore, vasodilatation due to FMD may affectthe estimation of blood pressure. Moreover, the importanceof viscoelasticity estimation considering the shape of thevessel is suggested. In the future, we plan to study theconstruction of a viscoelasticity estimation model to evaluate
the viscoelasticity during FMD.
Acknowledgments
KAKENHI 20H02156.

Fig. 3. (Color online) The elasticity (solid line) and viscosity (dashed line)
during the FMD measurement (a) at rest, (b) after recirculation.

resultant deformation due to the change in the vessel diameterby assuming that the circular shape of the artery wasmaintained. These results suggest that the shape of the arteryshould be considered in the viscoelasticity estimation in
addition to the accurate measurement of blood pressure.
To evaluate the endothelial function from the viscoelastic
properties, the circular arterial shape should be maintained
during the measurement. However, it is difﬁcult to maintainthe arterial shape during the measurement because the FMD
test requires more than 10 min and dilation of the artery
occurs. Therefore, in the future, it is important to develop a
new viscoelastic model by considering the cross-sectional
shape of the arteries.
As shown in Fig. 3(b), the estimated viscosity showed astable value for subject B, while the values showed large
variabilities for subjects A and C. The viscosity reﬂects thewidening of the hysteresis loop between the blood pressureand vessel diameter during one heartbeat. The viscosity
estimate became large when the diameter estimate did notThis work was partially supported by JSPS

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