Reprinted from

REGULAR PAPER

Improvement in Accuracy of Ultrasonic Measurement of Transient Change
in Viscoelasticity of Radial Arterial Wall Due to Flow-Mediated Dilation
by Adaptive Low-Pass Filtering
Kazuki Ikeshita, Hideyuki Hasegawa, and Hiroshi Kanai

Jpn. J. Appl. Phys. 51 (2012) 07GF14# 2012 The Japan Society of Applied Physics

Person-to-person distribution (up to 10 persons) by the author only. Not permitted for publication for institutional repositories or on personal Web sites.

REGULAR PAPER

Japanese Journal of Applied Physics 51 (2012) 07GF14
DOI: 10.1143/JJAP.51.07GF14

Improvement in Accuracy of Ultrasonic Measurement of Transient Change
in Viscoelasticity of Radial Arterial Wall Due to Flow-Mediated Dilation
by Adaptive Low-Pass Filtering
Kazuki Ikeshita1 , Hideyuki Hasegawa1;2 , and Hiroshi Kanai1;2 
12Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan

Received November 18, 2011; accepted February 27, 2012; published online July 20, 2012
In our previous study, the stress–strain relationship of the radial arterial wall was measured and the viscoelasticity of the intima–media region was
estimated from the stress–strain relationship. Furthermore, the transient change in viscoelasticity due to flow-mediated dilation (FMD) was
estimated by the automated detection of wall boundaries. In the present study, the strain rate was adaptively filtered to improve the accuracy ofviscoelasticity estimation by decreasing the high-frequency noise. Additionally, in a basic experiment, this method was validated using a silicone
tube (simulating artery). In the basic experiment, the elasticity was estimated with a mean error of 1.2%. The elasticity measured at each beam
position was highly reproducible among measurements, whereas there was a slight variation in measured elasticity among beams. Consequently,
in in vivo measurements, the normalized mean square error (MSE) was clearly decreased. Additionally, the stress–strain relationship of the radial
arterial wall was obtained and the viscoelasticity was estimated accurately. The inner small loop, which corresponds to the negative pressure
wave caused by the closure of the aortic valve, can be observed using the adaptive low-pass filtering (LPF). Moreover, the transient changes inthese parameters were similar to those in the previous study. These results show the potential of the proposed method for the thorough analysis of
the transient change in viscoelasticity due to FMD. # 2012 The Japan Society of Applied Physics

1. Introduction

Medical ultrasound is clinically used to make a diagnosis forvarious organs, and it can be repeatedly employed to conﬁrm
time-dependent changes of the targeted organs, because it isnoninvasive and relatively stress-free for patients. Ultrasound B-mode imaging is widely used for the morphologicaldiagnosis of the arterial wall. Additionally, as well as themorphology of the arterial wall, the viscoelasticity of thearterial wall and the condition of blood are also usefulmarkers for the diagnosis of atherosclerosis.1–6)
The quantitative assessment of atherosclerosis, which is
the main cause of circulatory diseases, is essential formaking an early diagnosis of such diseases. The endothelial
dysfunction is considered to be an initial step of atherosclerosis.7,8) Additionally, it has been reported that thesmooth muscle, which constructs the media of the artery,changes its characteristics owing to atherosclerosis.9) Consequently, it is important for an early preventive treatment tononinvasively assess the arterial wall properties, which are
the endothelial function and the mechanical property of themedia.
The arterial wall is composed of three layers, namely,
intima, media and adventitia, as shown in Fig. 1.10) The
intima, the innermost layer, is composed of endothelial cells
and an internal elastic layer. Endothelial cells react to theshear stress caused by blood ﬂow and produce nitric oxide(NO), which is known as a vasodepressor material. The
smooth muscle, which constructs the media, is the main
source of the viscoelasticity of the vessel wall. Therefore,
the dilation and contraction of the artery depend on thecharacteristics of the media. The smooth muscle is relaxed
as a result of the response to the produced NO. This function
is important for maintaining the homeostasis of the vascularsystem.11)
For the evaluation of the endothelial function, there is aconventional technique for measuring the transient change in
the inner diameter of the brachial artery caused by ﬂowE-mail address: hasegawa@ecei.tohoku.ac.jp

Fig. 1. Scheme of the arterial wall structure.4)

mediated dilation (FMD) after the release of avascularization.12–16) FMD, which is the ratio of the change in diameter
due to FMD to the original diameter, is related to thecardiovascular risk factor, such as the cerebral infarction anddiabetes, and, thus, it is considered to be a reference index of
circulatory diseases.17–19) However, this method cannot
directly evaluate the mechanical properties of the arterial
wall.
For a more sensitive and detailed evaluation of theendothelial function and mechanical property of the media,
we have proposed a new noninvasive method for themeasurement of the elasticity of the brachial artery20,21)
and the stress–strain relationship of the radial arterial wall.22)
Additionally, the viscoelasticity of the intima–media region
was estimated from the stress–strain relationship.23) In ourprevious study, the transient change in viscoelasticity due to
FMD was estimated by the automated detection of wallboundaries24) to reduce the operator dependence.
In the proposed method, it is necessary to measureviscoelasticity accurately and reproducibly to evaluate therate of change in viscoelasticity after avascularization.

07GF14-1# 2012 The Japan Society of Applied Physics

Person-to-person distribution (up to 10 persons) by the author only. Not permitted for publication for institutional repositories or on personal Web sites.

Jpn. J. Appl. Phys. 51 (2012) 07GF14

K. Ikeshita et al.

Therefore, in the present study, the strain rate was adaptively
ﬁltered to improve the accuracy of viscoelasticity estimation,
by decreasing the high-frequency noise ampliﬁed by thediﬀerentiation of the strain. Additionally, the proposed
method was validated using a silicone tube (simulatingartery) by evaluating the accuracy of the estimation ofviscoelasticity. Consequently, the proposed method wasapplied to the human radial artery and the transient change
in viscoelasticity due to FMD was measured.

(a)

2. Principles and Experimental Methods
2.1 Principles of estimating artery wall viscoelasticity
from measured stress–strain relationship anddecreasing high-frequency noise by filtering(b)

The detailed analysis of the change in the viscoelasticity of
the arterial wall due to FMD requires the in vivo measurement of the stress–strain relationship, which has not beenmeasured noninvasively thus far.
For the radial artery, the inner pressure can be noninvasively and continuously measured with a special sphygmometer (Colin JENTOW-7700). Thus, the waveform of
blood pressure pðtÞ can be obtained, and the viscoelasticity
can be estimated from the stress–strain relationship.22–24)
To determine the stress–strain relationship, the minutechange in the thickness (radial strain) hðtÞ of the rightradial arterial wall during a cardiac cycle was also measured
using the phased tracking method.25) Together with themeasurement of ultrasonic RF signals for the estimation ofhðtÞ, the waveform of blood pressure (stress) pðtÞ in the leftradial artery was continuously measured with the sphygmometer.
For the measurement of the change in thickness, thevelocities of artery wall boundaries [namely, the lumenintima boundary (LIB) and media-adventitia boundary(MAB)] were estimated. These boundaries were detectedby adaptive template matching15) and these velocities vðtÞwere estimated from the phase shift ðtÞ of RF echoes in
two consecutive frames. The phase shift ðtÞ was obtainedusing the complex cross-correlation applied to the quadrature demodulated signals of the measured RF echoes. Thechange in thickness, hðtÞ, between two diﬀerent depths, A
and B (corresponding to the LIB and MAB, respectively), in
the arterial wall along an ultrasonic beam was obtained fromthe diﬀerence between the displacements xLIB ðtÞ and xMAB ðtÞat these two positions as^ ¼ x^LIB ðtÞ  x^MAB ðtÞ
hðtÞ
Z tZ
½v^LIB ðtÞ  v^LIB ðtÞ dt:
¼

ð1Þ

0

The strain ðtÞ was obtained from the change in thickness,hðtÞ, which is divided by the intima–media thickness at thetime of the R-wave of the electrocardiogram. By assuming
the Voigt model as a viscoelastic model of the intima–media
region, the stress–strain relationship is given by_ þ 0 ;^ ðtÞ ¼ Es  ðtÞ þ   ðtÞ

ð2Þ

where ^ ðtÞ is the stress modeled by the Voigt model, and_ðtÞ, ðtÞ,
Es , and  are the strain, strain rate, static elasticity,and viscosity coeﬃcient, respectively. In the in vivo
measurement, the measured stress ðtÞ is the incremental
strain due to the pulse pressure, whereas the measured stressFig. 2. (Color online) (a) Waveforms and (b) power spectra of strain ratesof the arterial walls obtained with (blue) and without (black) ﬁltering.

includes the bias stress (diastolic blood pressure). Therefore,
0 is added to the right-hand side of eq. (2) as the bias stresscorresponding to the diastolic pressure.
In this study, the strain rate was ﬁltered to decrease thehigh-frequency noise ampliﬁed by the diﬀerentiation of thestrain. Figures 2(a) and 2(b) show the waveforms andspectra of the strain rates of the arterial walls obtained withand without ﬁltering. By a low-pass ﬁltering (LPF), theeq. (2) was rewritten by_^ LPF ðtÞ ¼ Es  ðtÞ þ   LPF½ðtÞþ 0 :

ð3Þ

The mean square error (MSE)  between the measuredðtÞ and model ^ LPF ðtÞ stresses is deﬁned by ¼ Et ½fðtÞ  ^ LPF ðtÞg2 ;ð4Þwhere Et ½ indicates the averaging operation during a
cardiac cycle. The parameters in eq. (3), Es , , and 0 , were
estimated by the least-squares method by minimizing thenormalized MSE  between the measured and modelstresses ðtÞ and ^ LPF ðtÞ. Additionally, the minimized MSEmin was calculated at each cutoﬀ frequency fc of LPF in therange from 5 to 160 Hz, and the cutoﬀ frequency, whichgave minimum min , was determined adaptively.
2.2 Procedure for basic experiment

In this study, we evaluated the accuracy of the estimation ofviscoelasticity by a basic experiment using a silicone tube
(simulating artery). The silicone tube (wall thickness: 1 mm;
inner diameter: 8 mm) includes graphite powder as scatterers, and we applied pulsatile ﬂow (simulating blood ﬂow)
for the induction of pulsatile change in wall thickness.

07GF14-2# 2012 The Japan Society of Applied Physics

Person-to-person distribution (up to 10 persons) by the author only. Not permitted for publication for institutional repositories or on personal Web sites.

Jpn. J. Appl. Phys. 51 (2012) 07GF14

K. Ikeshita et al.

Laser displacement gauge
tank for control of dilating pressure

rubber 8 cm
Laser displacement gauge

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

Fig. 4. (Color online) B-mode image of silicone tube.

In this experiment, we measured the changes in thickness
and inner pressure caused by the pulsatile ﬂow to obtain the
stress–strain relationship, and the viscoelasticity was estimated using the principles described in x2.1. Additionally,
for the evaluation of the accuracy of the proposed method,
we estimated the elasticity of the silicone tube from thechange in outer diameter, which was measured using alaser displacement gauge. Figure 3 shows the experimental
system, and the elasticity, which was estimated using a laser,
is deﬁned bycaused by internal pulsatile ﬂow (simulating blood ﬂow).
Figure 5 shows the results of the measurement of the change
in the thickness of the silicone tube. In the basic experiment,
the boundaries of the wall, which were tracked by the phase
tracking method, were determined automatically by thresholding to the echo amplitude.
Additionally, in this measurement, the strain rate wasﬁltered to decrease the high-frequency noise ampliﬁed by
the diﬀerentiation of the strain. Figure 6 shows the eﬀects of
LPF. Figure 6(a) shows the min at each cutoﬀ frequency fc ,and the adaptive cutoﬀ frequency f^c , which gives minimum
min , is adaptively determined ( fc ¼ 20 Hz in Fig. 6).
Figure 6(b) shows the strain rates obtained with and without
ﬁltering using the adaptive cutoﬀ frequency. Figures 6(c)and 6(d) show the estimated pressure and stress–strain
relationship, respectively. As shown in Fig. 6(b), the highfrequency noise was clearly decreased, and min was
decreased from 2.3 to 1.7%.
Moreover, for the evaluation of the accuracy of the
proposed method, we estimated the elasticity of the silicone
tube from the change in outer diameter, which was measured
using the laser displacement gauge. Figure 7 shows themeasured relationship between inner pressure and outer
diameter (15 cycles of the pulsatile ﬂow). The green line
shows the mean measured elasticity (467 kPa), which was
calculated using eq. (5).
Figure 8 shows the elasticity and viscosity of the silicone
tube, which were estimated by the proposed method. In theultrasound measurement, the mean elasticity was 472 kPa(mean viscosity was 8.67 kPas). The elasticity was estimated with a mean error of 1.2%.

Einc ¼

3 d02
p
;
2
2
2 de  d0 de ðtÞ=deð5Þwhere de ðtÞ and p indicate the changes in outer diameterand inner pressure, respectively. In the measurement using
the laser displacement gauge, the apparatus employed in thisstudy may have an undesirable time delay that would largely
aﬀect the estimation of the viscosity of the material.
Therefore, we evaluated only the elasticity measured byultrasound (Es ) by referring to the elasticity measured usinga laser (Einc ).
2.3 Procedure for in vivo experiment

In this study, the right radial arteries of healthy subjects
were measured. In this measurement, ultrasonic RF echoes(transmit center frequency: 22 MHz) were acquired at asampling frequency of 66.5 MHz for 2 s at a frame rate ofabout 320 Hz. At the same time, the waveform of bloodpressure on the left radial artery was continuously measured
with a sphygmometer.
We applied this method to a healthy subject and evaluate
the eﬀect of ﬁltering. Consequently, we measured thetransient change in viscoelasticity due to FMD. Thisacquisition was repeated at every 20 s for 2 min at rest
before avascularization and every 12 s for 3 min afterrecirculation.
3. Results
3.1 Results of basic experiment

For the validation of the method, we applied the proposed
method to a silicone tube (simulating artery), and Fig. 4
shows the B-mode image of the anterior wall of the tube. We
measured the change in the thickness of the anterior wall

3.2 Results of in vivo experiment

RF data for 2 s was obtained by each acquisition to include atleast an entire cardiac cycle. Therefore, the changes inthickness and blood pressure were obtained for at least one
cardiac cycle in each measurement for estimating theviscoelastic parameters of the radial arterial wall.
Figure 9 shows the eﬀects of LPF in the in vivo
measurement. As shown in Fig. 9(a), the normalized
residual MSE min was decreased from 8.9 to 1.2% byadaptive LPF ( fc ¼ 12:3 Hz). Figure 9(b) shows the measured and estimated pressures. Figure 9(c) shows the stress–

07GF14-3# 2012 The Japan Society of Applied Physics

Person-to-person distribution (up to 10 persons) by the author only. Not permitted for publication for institutional repositories or on personal Web sites.

Jpn. J. Appl. Phys. 51 (2012) 07GF14

K. Ikeshita et al.

µmµm
Fig. 5. (Color online) Results obtained for anterior wall of silicone tube (simulating artery). (a) M-mode image. (b) Trigger signal of pump. (c) Innerpressure. (d) Estimated velocities of line k. (e) Estimated velocities of line l. (f ) Change in thickness.

Fig. 6. (Color online) (a) Residual MSE min at each cutoﬀ frequency. (b) Strain rates obtained with and without ﬁltering using adaptive cutoﬀ frequency( fc ¼ 20 Hz). (c) Estimated pressure. (d) Stress–strain relationship.

strain relationship of the radial arterial wall during aheartbeat. The red line shows the hysteresis loop (reference)measured using a sphygmometer. The black and blue lines inFig. 9(c) show the estimated loops obtained without andwith ﬁltering, respectively. Additionally, the inner smallloop, which corresponds to the negative pressure wave
caused by the closure of the aortic valve, can be observed byadaptive LPF.
Figure 10 shows the transient change in min between themeasured and model stresses ðtÞ and ^ LPF ðtÞ. min was

07GF14-4# 2012 The Japan Society of Applied Physics

Person-to-person distribution (up to 10 persons) by the author only. Not permitted for publication for institutional repositories or on personal Web sites.

Jpn. J. Appl. Phys. 51 (2012) 07GF14

K. Ikeshita et al.

(a)

(b)

Fig. 7. (Color online) Relationship between inner pressure and outer
diameter. A mean elasticity of 467 kPa was obtained from the slope of theregression line (green line).

(c)Fig. 8. (Color online) Means and standard deviations of measured elastic
moduli and viscosity constants of the silicone tube. The red line shows themean elasticity measured using a laser. The blue lines show the means ofstatic elasticity and viscosity measured using ultrasound.

clearly decreased by adaptive LPF. In particular, the MSE
obtained after the release of the cuﬀ was decreased
signiﬁcantly.
Figure 11 shows the transient change in viscoelasticity
due to FMD. After the release of the cuﬀ, a temporaldecrease in elasticity and a temporal increase in viscosity
were measured. The transient changes in these parameters
were similar to those in the previous study.22)
4. Discussion

In this study, we evaluated the accuracy of the estimation ofviscoelasticity by a basic experiment using a silicone tube

Fig. 9. (Color online) (a) Residual MSE min at each cutoﬀ frequency.
(b) Estimated pressures obtained with and without ﬁltering using adaptive
cutoﬀ frequency ( fc ¼ 12:3 Hz). (c) Measured stress–strain relationships
obtained and estimated stress–strain relationship with and without ﬁltering.

(simulating artery). In Fig. 8, the elasticity is estimated witha small error (mean error of 1.2%, which is about 5 kPa).
However, there are relatively large standard deviations.
Figure 12 shows the elasticity measured at each beam
position. As shown in Figs. 8 and 12, the measured elasticity
values ﬂuctuate among beams. However, the reproducibilityof elasticity and the small ﬂuctuation in elasticity aremeasured at the same position. Therefore, it is required thatthe variation in the viscoelasticity of the silicone tube should
be further investigated. Moreover, the accuracy of theestimation of elasticity and reproducibility is demonstrated
in this validation experiment.
Figure 9 shows the stress–strain relationship of the radial
arterial wall during a heartbeat. As shown in Figs. 6(d) and07GF14-5# 2012 The Japan Society of Applied Physics

Person-to-person distribution (up to 10 persons) by the author only. Not permitted for publication for institutional repositories or on personal Web sites.

Jpn. J. Appl. Phys. 51 (2012) 07GF14

K. Ikeshita et al.

without filteringwith filtering

Fig. 10. (Color online) Transient change in min for a healthy subject.

Fig. 12. (Color online) Mean elasticity measured at each beam position.

viscosity

elasticity

Fig. 11. (Color online) Transient change in viscoelasticity of the radial
arterial wall due to FMD.

9(c), LPF decreases the high-frequency noise clearly andimproves the accuracy in of the estimation of each parameter(corresponds to the shape of hysteresis). In particular, in thein vivo measurement, the inner small loop that corresponds
to the negative pressure wave can be observed. Although theamplitude of this negative pressure wave is smaller than thatof the positive pressure wave, it is an important component
in vascular dynamics. The negative pressure wave iscomposed of high frequency components compared withthe positive pressure wave. Therefore, the cutoﬀ frequency
of LPF should be determined not to remove the componentof the negative pressure wave.
As shown in Fig. 9(c), the duration of the inner smallloop is about 0.22 s [corresponds to the 2nd peak of bloodpressure in Fig. 9(b) and the reciprocal of the duration isabout 4.6 Hz]. Additionally, the main component of bloodpressure waveform is about 1 Hz (corresponds to a cardiac
cycle). The adaptive cutoﬀ frequency is determined byevaluating the MSE using both components because suchcomponents are important in the arterial dynamics. As
shown in the example in Fig. 9(a), the determined adaptive
cutoﬀ frequency is much higher (12.3 Hz) than 4.6 Hz topreserve the negative pressure component. As shown in
Fig. 9(c), the estimated hysteresis loop is signiﬁcantly
deformed (at fc ¼ 5 Hz) when the cutoﬀ frequency is not
adaptively determined and is very low.
The shape of the stress–strain relationship includes muchinformation. For example, the slope shows the elastic
modulus, and the area depends on the ratio of the loss
modulus to the static elastic modulus when the Voigt modelis assumed. Therefore, the accurate measurement of thestress–strain relationship is very important for the detailed

Fig. 13. (Color online) Means of min obtained with and without LPF
before and after avascularization.

analysis of viscoelasticity. Additionally, Fig. 13 shows thecomparison of the means of min obtained with and without
LPF before and after avascularization. As shown in Figs. 10
and 13, the min obtained after avascularization was larger
than that obtained before avascularization. To evaluate
FMD, stable measurements are necessary to evaluate thechange in the viscoelasticity of the radial arterial wall.
Therefore, the reduction in min by LPF, particularly during
FMD (after avascularization), signiﬁcantly contributes to themeasurement of the change in viscoelasticity.
5. Conclusions

In this study, we evaluated the accuracy of the estimationof viscoelasticity by a basic experiment using a silicone
tube (simulating artery). In the basic experiment, theaccuracy of reproducibility in the estimation of elasticity
was demonstrated. Additionally, in the in vivo measurement,
the normalized MSE min was clearly decreased, and theinner small loop, which corresponds to the negative pressure
wave caused by the closure of the aortic valve, was also
observed by adaptive LPF. These results show the potentialof the proposed method for the thorough analysis of thetransient change in viscoelasticity due to FMD.
Acknowledgment

This work was supported by a Grant-in-Aid for JSPS
Fellows (21-3796).

07GF14-6# 2012 The Japan Society of Applied Physics

Person-to-person distribution (up to 10 persons) by the author only. Not permitted for publication for institutional repositories or on personal Web sites.

Jpn. J. Appl. Phys. 51 (2012) 07GF14

K. Ikeshita et al.

1) K. Tuzuki, H. Hasegawa, and H. Kanai: Jpn. J. Appl. Phys. 47 (2008) 4180.
2) D. G. Paeng, R. Y. Chiao, and K. K. Shung: Ultrasound Med. Biol. 30(2004) 815.
3) N. Saitoh, H. Hasegawa, and H. Kanai: Jpn. J. Appl. Phys. 48 (2009)
4)
5)
6)
7)
8)
9)
10)
11)
12)

13)

14)

15)

07GJ08.
T. Fukushima, H. Hasegawa, and H. Kanai: Jpn. J. Appl. Phys. 50 (2011)
07HF02.
S. Satomura: J. Acoust. Soc. Am. 29 (1957) 1181.
H. Hasegawa and H. Kanai: IEEE Trans. Ultrason. Ferroelectr. Freq.
Control 55 (2008) 2626.
R. Ross: New Engl. J. Med. 340 (1996) 115.
M. Walski, S. Chlopicki, R. Celary-walska, and M. Frontczak-baniewicz:
J. Physiol. Pharmacol. 53 (2002) 713.
Y. Matsuzawa: Nippon Rinsho 51 (1993) 1951 [in Japanese].
A. E. Medvedev, V. I. Samsonov, and V. M. Fomin: J. Méc. Théor. Appl.
47 (2006) 324.
P. M. Vanhoutte: J. Clin. Invest. 107 (2001) 23.
D. S. Celermajer, K. E. Soresen, V. M. Gooch, D. J. Spiegelhalter, O. I.
Miller, J. D. Sullivan, J. K. Lloyd, and J. E. Deanﬁeld: Lancet 340 (1992)
1111.
M. C. Corretti, T. J. Anderson, E. J. Benjamin, D. Celermajer, F.
Charbonneau, M. A. Creager, J. Deanﬁeld, H. Drexler, M. GerhardHerman, D. Herrington, P. Vallance, J. Vita, and R. Vogel: J. Am. Coll.
Cardiol. 39 (2002) 257.
J. Deanﬁeld, A. Donald, C. Ferri, C. Giannattasio, J. Halcox, S. Halligan,

16)
17)
18)
19)
20)
21)
22)
23)
24)
25)

07GF14-7

A. Lerman, G. Mancia, J. J. Oliver, A. C. Pessina, D. Rizzoni, G. P. Rossi,
A. Salvetti, E. L. Schiﬀrin, S. Taddei, and D. J. Webb: J. Hypertension 23(2005) 7.
N. M. De Roos, M. L. Bots, E. G. Schouten, and M. B. Katan: UltrasoundMed. Biol. 29 (2003) 401.
M. Nishino: Cho-onpa Igaku 37 (2010) 243 [in Japanese].
D. R. Witte, J. Westerink, E. J. de Koing, Y. van der Graaf, D. E. Grobbee,
and M. L. Bots: J. Am. Coll. Cardiol. 45 (2005) 1987.
P. C. Lavallee, P. Bonnin, J. Labreuche, P. Amarenco, and B. Lévy:
Ultrasound Med. Biol. 32 (2006) 1165.
R. Ravikumar, R. Deepa, C. S. Shanthirani, and V. Mohan: Am. J. Cardiol.
90 (2002) 702.
T. Kaneko, H. Hasegawa, and H. Kanai: Jpn. J. Appl. Phys. 46 (2007)
4881.
M. Sugimoto, H. Hasegawa, and H. Kanai: Jpn. J. Appl. Phys. 44 (2005)
6297.
K. Ikeshita, H. Hasegawa, and H. Kanai: Jpn. J. Appl. Phys. 47 (2008)
4165.
K. Ikeshita, H. Hasegawa, and H. Kanai: Jpn. J. Appl. Phys. 48 (2009)
07GJ10.
K. Ikeshita, H. Hasegawa, and H. Kanai: Jpn. J. Appl. Phys. 50 (2011)
07HF08.
H. Kanai, M. Sato, Y. Koiwa, and N. Chubachi: IEEE Trans. Ultrason.
Ferroelectr. Freq. Control 43 (1996) 791.

# 2012 The Japan Society of Applied Physics