Sensors and Actuators A 286 (2019) 146–151

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Sensors and Actuators A: Physicaljournal homepage: www.elsevier.com/locate/sna

Blood pressure measurement using piezoelectric effect by an
ultrasonic probe
Mototaka Arakawa a,b,∗ , Kota Kudo b , Kazuto Kobayashi c , Hiroshi Kanai a,babcGraduate School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
Honda Electronics Co. Ltd., Toyohashi 441-3193, Japana r t i c l e

i n f oArticle history:
Received 1 August 2018
Received in revised form
28 November 2018
Accepted 16 December 2018
Available online 17 December 2018
Keywords:
Radial artery
Blood pressure
Diameter
Piezoelectric effectViscoelasticity
Ultrasonic probea b s t r a c t
An ultrasonic method to measure the changes in radial arterial diameter and blood pressure in a noninvasive manner was proposed to estimate viscoelastic characteristics of the arterial wall to diagnose vascularendothelial dysfunction at an extremely early stage. In the present study, a measurement method of bloodpressure using the piezoelectric effect of the ultrasonic probe was investigated. At ﬁrst, blood pressure
waveform measured by the piezoelectric element was discussed using piezoelectric constitutive equations. We conﬁrmed that the blood pressure waveform can be obtained by integrating the waveform
measured by the piezoelectric element. Then, a conventional ultrasonic probe was modiﬁed to measure a blood pressure waveform and the measurement is demonstrated. Changes in the radial diameter
was also measured using an ultrasonic diagnosis equipment with a conventional linear ultrasonic probe.
The measured voltage by the piezoelectric element was of the same order as the result estimated fromthe theoretical consideration with typical material constants of the piezoelectric element. The diameter
expanded with an increase in blood pressure and then gradually returned due to the decrease in bloodpressure with viscosity. From the relationship between the arterial diameter and blood pressure, thehysteresis characteristic of the artery wall during one heartbeat was conﬁrmed.
© 2018 Elsevier B.V. All rights reserved.

1. Introduction
Recently, the occurrence of cardiovascular diseases, such asheart disease and cerebrovascular disease has been increasing,accounting for 23.5% of the causes of death in Japan in 2016 [1].
Arteriosclerosis is the main factor of these cardiovascular diseases,
and diagnostic techniques, such as X-ray imaging and intravascular ultrasound, are clinically used. However, iterative diagnoses bythese methods are difﬁcult because of their invasive nature. Therefore, it is important to develop a noninvasive diagnostic method for
diagnoses.
As noninvasive diagnostic methods, Wetter and Kenner [2] andMcDonald et al. [3] proposed an index of pulse wave velocity(PWV), and Weitz et al. [4] proposed an ankle brachial index (ABI).
However, these are indicators for diagnosing irreversibly advanced
lesions and are not suitable for diagnosis at an extremely early stageof arteriosclerosis. At such an extremely early stage before plaquesappear, vascular endothelial functions decrease, but will recover∗ Corresponding author.
E-mail address: arakawa@ecei.tohoku.ac.jp (M. Arakawa).
https://doi.org/10.1016/j.sna.2018.12.019
0924-4247/© 2018 Elsevier B.V. All rights reserved.

because of reversible lesions [5,6]. Therefore, in order to diagnose
and treat arteriosclerosis at an extremely early stage, developmentof a noninvasive diagnostic method to evaluate vascular endothelial
functions is crucial.
Vascular endothelial functions are functions of endothelial cells
to react to shear stress caused by blood ﬂow and generate nitricoxide (NO), which stimulates and relaxes the blood vessel wall
[7,8]. Vascular endothelial functions are conventionally evaluatedby measuring the change in the inner diameter of the brachial arteryby the ﬂow-mediated dilation (FMD) method [9–11]. However, it
is difﬁcult to accurately evaluate vascular endothelial function by
the FMD method [12,13], because the rate of change in the vessel
diameter is only ∼6% in healthy subjects.
Some methods based on the velocity dispersion of shear waves
were developed as noninvasive evaluation methods of the elasticity
of arteries and soft tissue [14–16]. Noninvasive evaluation methods
based on force and displacement hysteresis characteristics weredeveloped to evaluate viscoelasticity [17].
In our group, the viscoelastic parameters, viz., stiffness parameter ␤ and viscosity parameter ␩, were estimated by the stress-strain
characteristics obtained by measuring a relationship between
blood pressure and wall thickness [18–23]. We also estimatedM. Arakawa et al. / Sensors and Actuators A 286 (2019) 146–151

the temporal change of ␤ and ␩ by simultaneously measuringchanges in arterial diameter and the blood pressure during vascular relaxation reaction [24]. Comparing the results before and after
a vascularization suggested the possibility of evaluating the vascular endothelial functions and the viscoelasticity of blood vessels.
However, the arterial diameter and blood pressure were measured
at different positions, and the delay time between the pressure sensor and the ultrasonic probe were estimated and corrected to use as
the measurements at the identical position. However, the hysteresis characteristics of the blood vessel wall could not be accurately
estimated since the delay time changes during a heartbeat becauseof PWV changes caused by changes in blood pressure, causing anerror in the delay time estimation.
In order to solve this problem, it is ideal to measure the arterial diameter and blood pressure simultaneously at an identical
position by a single ultrasonic probe. For measurement, it is necessary to investigate whether a conventional ultrasonic probe can beused as a blood pressure sensor utilizing the piezoelectric effect inadvance. This is because the frequency ranges of ultrasonic probes
are much higher than that of the blood pressure waveform, which
is mainly less than 12 Hz [25]. In this basic study, ﬁrst, the frequency characteristic of the output voltage from a piezoelectricelement was theoretically derived using piezoelectric constitutive equations and material parameters of an ultrasonic probe.
Then, a conventional ultrasonic probe was modiﬁed to measure theblood pressure waveform and the measurement is demonstrated.
Changes in the radial diameter was also measured using an ultrasonic diagnosis equipment with a conventional linear ultrasonicprobe. As a result, the hysteresis characteristic of the blood vessel
wall is estimated.
2. Principle and method

In order to measure the arterial diameter and the blood pressure at an identical position, it is necessary to transmit and receive
ultrasonic waves and to detect the blood pressure using only asingle ultrasonic probe. This will be realized if the blood pressure waveform is measured using the piezoelectric effect because
piezoelectric elements are generally used for the ultrasonic probe.
However, the frequency of a blood pressure waveform is lower thanapproximately 12 Hz [25] and far outside the bandwidth (usually
several to 10 MHz) of ultrasonic probes. Therefore, it is necessary toinvestigate whether blood pressure can be detected with enoughvoltage by the piezoelectric elements of the ultrasonic probe.
The piezoelectric constitutive equations are as follows:
E

Fig. 1. Schematic view of voltage generation at a piezoelectric element by applying
force.

z-axis were assumed to be 0. Thus, the following equations can beobtained from Eqs. (1) and (2):E
T1 = c13
S3 − e31 E3 ,(3)E
T2 = c13
S3 − e31 E3 ,(4)E
T3 = c33
S3 − e33 E3 ,(5)

D3 = e33 S3 + εS33 E 3 .

(6)

The following relationship among D3 , T3 , and E3 can be derived
by eliminating S3 from Eqs. (5) and (6):D3 =2.1. Measurement by piezoelectric effect

T = c : S − e · E,

(1)

D = e : S + εS · E,

(2)

where cE , e, and ␧S are the tensors of elastic constant under constantelectric ﬁeld, piezoelectric constant, and permittivity under constant stress, respectively; and T, S, D, and E are the tensors of stress,
strain, dielectric displacement, and electric ﬁeld, respectively.
Lead zirconate titanate (PZT) ceramic has a perovskite structure,and the independent components of elastic constants, piezoelectric
constants, and permittivity are the same as those of class 6 mm ofthe hexagonal system [26]. The coordinate system for the piezoelectric element with width w, length l, and thickens h, is shown in
Fig. 1, where P means spontaneous polarization. Voltage V occurs
when the force F is applied to the piezoelectric element.
It is assumed that there is no strain along the horizontal directions because the piezoelectric elements used in the ultrasonicprobe are usually ﬁxed putting into a casing. That is, strain components other than S3 which corresponds to the strain along the

147

e33
E
c33

e2
T3 + ( 33+ εS33 )E3 .
E
c33

(7)

The electric charge Q generated at the piezoelectric element canbe obtained by the surface integral of dielectric displacement D3 by
the following equation:
Q = wlD3(8)

The relationship between the force F and the stress T3 is as follows:
F = wlT3(9)The capacity of the piezoelectric element Cd is expressed by thefollowing equation:
Cd =εS33 wlh(10).

The relationship between voltage V and electric ﬁeld E3 is asfollows:
V =E 3 h.

(11)

The following equation can be derived by substituting D3 in Eq.
(7) into Eq. (8) using Eqs. (9) – (11):
Q =

e33
E
c33

F+

D
c33
E
c33

Cd V,

(12)

D is the elastic constant at constant electric displacement,
where c33
E :and has the following relationship with c33
D
E
c33
= c33
+

2
e33

εS33

.

(13)

Next, let us consider the measurement of electric charge Q by
the voltmeter with input resistance R. The current ﬂowing from the148

M. Arakawa et al. / Sensors and Actuators A 286 (2019) 146–151

transducer I is the derivation of the electric charge Q. The following
equation can be obtained from Eq. (12):
I=

cD
dQ
dV
e33 dF
Cd
= E ·
+ 33
.
E
dt
dt
dt
c
c
33

(14)

33

The output voltage V is obtained by the following equation:
cDdV
e33 dFV = RI = R( E ·
Cd
+ 33
).
E
dt
dt
c33
c33

(15)

Treat the force F and the voltage V at each frequency component
f as follows:
F(f ) = F0 (f ) · ejωt ,(16)

V (f ) = V0 (f ) · ejωt ,(17)where ␻ is angular frequency. From Eq. (15), V0 (f) and F0 (f) havethe following relationship:ecjωR 33E

V0 (f ) =33

F0 (f ) .

cD

(18)

1 − jωR 33
E Cd
c

33

The transfer function G(f) {= F0 (f)/V0 (f)} from the applied force
to the output voltage, and the amplitude |G(f)| and phase ∠G(f) are
expressed as follows:

G (f ) =ecjωR 33E

V0 (f )=
F0 (f )

33cD

1 + jωR 33
E Cd



c

33

1 + ωR
e
c



cD
33
cE
33

2

,

(19)

Cd
Fig. 2. (a) Amplitude and phase of transfer function of a piezoelectric element. (b)Transfer function of the output voltage.

ωR 33
E



G (f ) = 



33

cD

1 + ωR 33
E Cd

2 ,

(20)
The following equation is obtained by applying the inverse
Laplace transform of Eq. (22):

c

33

1

∠G (f ) = −
ωR

.

cD
33
cE
33

(21)

Cd



cD

F0 (f ) =

c

33

e
c

jωR 33
E
33

1
e
R 33
cE
33

The calculated result of the transfer function G(f) is shownin Fig. 2 (a), obtained using the following typical parameSE = 1.28 × 1011 N/m2 , e2ters: c33
33 = 25.9 C/m , ε33 /ε0 = 2, 021,3
 = 7, 500 kg/m , R = 1 M˝, w = 0.2 mm, l = 4.0 mm, and h =3.2 mm. These parameters are the material constants of piezoelectric elements used in the present study. The gain increased with
20 dB/decade in the frequency ranges lower than 1000 Hz.
Assuming the difference of the systolic and diastolic arterialpressures is 50 mmHg, stress T3 is obtained as 6.67 × 103 N/m2 fromthe pressure difference. Then, F is obtained as 5.33 × 10−3 N from
Eq. (9). The transfer function of the output voltage of the received
signal is shown in Fig. 2(b). If the main frequency component of
the blood pressure waveform is several Hz, the gain is obtained
as approximately -90 dBV (0.03 mV) from Fig. 2(b). As shown in
Fig. 2, the zero-frequency component of the applied force cannot
lead to the generation of voltage. It is also understood from the factthat voltage is obtained by varying the force on the piezoelectricmaterials.
In this method, it is necessary to convert the measured voltage
V into force F (blood pressure). The force F0 (f) is expressed using
V0 (f) of Eq. (18) as follows:
1 − jωR 33
E Cd

f (t) =

V0 (f ) =1ecjωR 33
E
33

− Cd

D
c33

e33



 t

cD
V () d − Cd 33 V (t) + f0 ,
e33
0

(23)

where f0 is force at t = 0.
Using the above parameters of the probe, the coefﬁcients of
the ﬁrst and second terms of the right-hand side of Eq. (23) wereE ) = 4.95 × 103 N/( · m) and C c D /ecalculated as 1/(Re33 /c33
=
d 33
33

3.00 × 10−1 s · N/( · m), respectively. Therefore, the ﬁrst term isdominant in Eq. (23), and the blood pressure f(t) can be obtainedby integrating the measured voltage V(t), as follows:
f (t) =

1
e
c

R 33
E
33

 t

V () d + f0 .

(24)

0

To obtain the blood pressure waveform, it is necessary to calibrate f(t) by the systolic blood pressure psys and diastolic bloodpressure pdia . The calibrated blood pressure waveform p̂ (t) isexpressed as follows:p̂ (t) =psys − pdia
fmax − fmin

f (t) − fmin

+ pdia ,(25)

where fmax and fmin are the maximum and minimum values of f (t).
This calibration is needed for each measurement because the zerofrequency component of f(t) depends on pdia .
2.2. Experimental equipment and procedure

V0 (f ) .

(22)

In this study, two ultrasonic probes were prepared. One is aconventional linear array probe and another is a modiﬁed ultra-

M. Arakawa et al. / Sensors and Actuators A 286 (2019) 146–151

149

Fig. 4. B-mode image of the left radial artery.

3. Results and discussion

Fig. 3. (a) Schematic view of radial arterial diameter measurement by ultrasound,and (b) schematic view of radial arterial pressure measurement using the piezoelectric effect.

sonic probe to measure blood pressure waveforms. The changes indiameter and blood pressure were measured by ultrasound and thepiezoelectric effect using the conventional linear array probe andmodiﬁed ultrasonic probe, respectively, at different timings at an
identical position in the left radial artery of a 23-year-old healthymale.
An ultrasonic diagnostic apparatus (Hitachi Aloka, ProSound
F75) and a conventional linear array probe with 128 channels anda center frequency of 7.5 MHz were used for the measurement of
the change in diameter. The change in diameter and electrocardiogram (ECG) were measured at a sampling frequency of 40 MHz
and a frame rate of 252 Hz. The boundaries between the lumen
and the anterior and posterior walls were manually determinedfrom the received RF signal. The phased-tracking method [27–30]
was applied to the determined boundary to estimate the change indiameter.
We modiﬁed a linear ultrasonic probe so that the blood pressure
can be measured. The size of each rectangular piezoelectric element
was 4 × 0.2 × 3.2 mm3 . To enhance the output voltage, 10 elements
around the center of the ultrasonic probe were connected in parallel and these were used as a pressure sensor to measure the bloodpressure waveform by the piezoelectric effect. The blood pressure
waveform was measured at the same position as the ultrasonicmeasurement, and it was ﬁltered with a low-pass ﬁlter having acutoff frequency of 30 Hz and ampliﬁed with an ampliﬁer having anampliﬁcation factor of 10. Therefore, the output voltage is expected
to be approximately 3 mV. Moreover, the ECG was simultaneously
measured by an electrocardiograph (Nihon Kohden Corp., ECG1350). To calculate the blood pressure, systolic blood pressure psysand diastolic blood pressure pdia were measured in the right radial
artery by tonometry (Nihon Kohden Corp., JENTOW-7700).
Fig. 3 (a) and (b) shows schematic diagrams of measurementsof changes in diameter and blood pressure, respectively. Virtual
simultaneous measurement was realized by referring to the timeof the R wave of the ECG in each measurement and correcting thetiming of both waveforms of the change in diameter and the bloodpressure.

The B-mode image of the left radial artery is shown in Fig. 4.
The diameter of the artery was determined by using three beams
passing near the center of the artery as shown with red lines inFig. 4.
The measured blood pressure waveform using this probe isshown with a dashed line in Fig. 5. The obtained amplitude of V(t)in Eq. (24) was approximately 12 mV. The obtained waveform was
ﬁltered with moving average to suppress noise components. The
systolic and diastolic blood pressures were measured as 114 and
61 mmHg by tonometry, respectively. The measured output was ofthe same order as the theoretical one. The time-integrated waveform f(t) of Eq. (24) is shown with a solid red line in Fig. 5. It was
conﬁrmed that it resembles the typical blood pressure waveform
measured by the tonometry in the radial artery, as shown with theblue line in Fig. 5. The effect of the frequency dependence of gain
shown in Fig. 2 could be small because the frequency components ofthe blood pressure waveform in the frequency range of 0.9–6.0 Hz
was constituted 50% of the amplitude spectrum [25]. The timingof measurement results of the change in diameter and the bloodpressure waveform were synchronized with reference to the time

Fig. 5. Waveform measured by the piezoelectric effect (red dashed line), timeintegrated waveform for the measured waveform (red solid line), and blood pressure
waveform measured by the tonometry (blue line) (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of thisarticle).

150

M. Arakawa et al. / Sensors and Actuators A 286 (2019) 146–151

ultrasonic probe that can measure blood pressure and the change
in diameter simultaneously.

4. Conclusions

Fig. 6. Measurements for the change in diameter and blood pressure waveform by
the piezoelectric effect with reference to the time of the R wave of the ECG.

of the R wave of the ECG. Little temporal error was observed in therise of waveforms to a change in diameter and blood pressure.
Fig. 6 shows the results of blood pressure waveforms for threeheartbeats and a diameter. Similar results were obtained among
three heartbeats. The relationship between blood pressure and thechange in arterial diameter is shown in Fig. 7. The hysteresis characteristics were conﬁrmed as that the diameter expanded linearlywith an increase in the blood pressure and then gradually returned
with a decrease in blood pressure due to the viscosity. This showsthat the elasticity of the arterial wall was dominant at the time ofvasodilatation; otherwise the viscosity also inﬂuences the recovery.
Therefore, relationships from the blood pressure to the change indiameter were successfully obtained by measuring the blood pressure waveform by the piezoelectric effect of the ultrasonic probe.
The viscoelastic parameters, viz., the stiffness parameter ␤ andviscosity parameter ␩, were estimated by the least squares method
assuming the Voigt model [24,31,32]. The stiffness parameters
␤ were 5.2 × 102 , 4.5 × 102 , and 6.6 × 102 kPa, and the viscosity
parameters ␩ were 1.4, 2.0, and 2.6 kPa·s, for the 1st, 2nd, and 3rdheartbeats, respectively. The variations of the viscoelastic parameters were relatively large because the blood pressure waveform
and the change in diameter were not measured at the same time.
The reproducibility will be improved by the development of a new

Fig. 7. Relationship between blood pressure and arterial diameter.

In this study, blood pressure waveforms measured using thepiezoelectric effect by an ultrasonic probe was discussed. First,
the waveform obtained by a piezoelectric element was discussed
using piezoelectric constitutive equations, and we conﬁrmed thatthe blood pressure waveform can be obtained by integrating the
waveform measured by the piezoelectric element. An ultrasonicprobe was modiﬁed to measure blood pressure waveforms. The
measured voltage by the piezoelectric element was of the sameorder as the result estimated from the theoretical consideration andmaterial constants of the piezoelectric element. Therefore, we conﬁrmed that it is possible to measure the blood pressure waveformby ultrasonic probes using piezoelectric effect. Changes in the radial
diameter was also measured using an ultrasonic diagnosis apparatus with a conventional linear ultrasonic probe. We observed thatthe timing of the rise of the blood pressure waveform and that of
the change in diameter was almost same, referring to the R waveof the ECG. We successfully conﬁrmed that the hysteresis characteristic in the radial artery during one beat was obtained from themeasured blood pressure and the change in diameter. Therefore,
there is a possibility of evaluating vascular endothelial functionsof the arterial wall by measurements of the blood pressure waveform using an ultrasonic probe. We developed an ultrasonic probe
for simultaneously measuring blood pressure and diameter. In a
future study, we will perform simultaneous measurement by using
this probe.

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Biographies
Mototaka Arakawa received the B.E., M.E., and Ph.D. degrees in electrical engineering from Tohoku University, Sendai, Japan, in 1993, 1995, and 2000, respectively.
He is currently an associate professor at the Graduate School of Biomedical Engineering, Tohoku University. His research interests include developments of theultrasonic transducer and the acoustic microscopy for tissue and cell characterization and the application of the line-focus-beam ultrasonic material characterization
system.
Kota Kudo received the B.E. and M.E. degrees in electronic engineering from Tohoku
University, Sendai, Japan, in 2016 and 2018, respectively. He is currently working
at Sharp Corporation. His research interests include development of the ultrasonicprobe.
Kazuto Kobayashi received B.E. degree in electrical engineering from Shibaura
Institute of Technology, in 1976. He received Ph.D. degrees in 2011 from Tohoku
University. He is currently a director of Department of Research and Development at
Honda Electronics Co. Ltd. in Toyohashi, Japan. His research activities and interests
include medical ultrasound imaging, signal processing and high frequency ultrasound transducers.
Hiroshi Kanai received a B.E. degree from Tohoku University, Sendai, Japan,
in 1981, and M.E. and the Ph. D. degrees, also from Tohoku University, in
1983 and in 1986, both in electrical engineering. He is currently a professor
in the Department of Electronic Engineering, Graduate School of Engineering,Tohoku University. His present interests are in transcutaneous measurementof the heart wall vibrations and myocardial response to propagation of electrical potential and cross-sectional imaging of elasticity around atherosclerotic
plaque with transcutaneous ultrasound for tissue characterization of the arterial
wall.