Japanese Journal of Applied
Physics

Related content

REGULAR PAPERS

Local pulse wave velocity estimated from small
vibrations measured ultrasonically at multiple
points on the arterial wall

- Correction of change in propagation timedelay of pulse wave during flow-mediateddilation in ultrasonic measurement ofarterial wall viscoelasticity
Mitsuki Sato, Hideyuki Hasegawa andHiroshi Kanai

To cite this article: Mika Ito et al 2018 Jpn. J. Appl. Phys. 57 07LF14- Experimental study on the pressure wave
propagation in the artificial arterial tree inbrain
Shinya Shimada, Ryo Tsurusaki, Fumiaki
Iwase et al.

View the article online for updates and enhancements.

- Accurate evaluation of viscoelasticity ofradial artery wall during flow-mediateddilation in ultrasound measurement
Yasumasa Sakai, Hirofumi Taki andHiroshi Kanai

This content was downloaded from IP address 130.34.32.223 on 12/06/2018 at 06:18

REGULAR PAPER

Japanese Journal of Applied Physics 57, 07LF14 (2018)https://doi.org/10.7567/JJAP.57.07LF14

Local pulse wave velocity estimated from small vibrations measured ultrasonicallyat multiple points on the arterial wall
Mika Ito1, Mototaka Arakawa1,2, and Hiroshi Kanai2,1*
1

Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan2*E-mail: kanai@ecei.tohoku.ac.jp
Received November 6, 2017; accepted February 4, 2018; published online June 11, 2018
Pulse wave velocity (PWV) is used as a diagnostic criterion for arteriosclerosis, a major cause of heart disease and cerebrovascular disease.
However, there are several problems with conventional PWV measurement techniques. One is that a pulse wave is assumed to only have an
incident component propagating at a constant speed from the heart to the femoral artery, and another is that PWV is only determined from acharacteristic time such as the rise time of the blood pressure waveform. In this study, we noninvasively measured the velocity waveform of small
vibrations at multiple points on the carotid arterial wall using ultrasound. Local PWV was determined by analyzing the phase component of thevelocity waveform by the least squares method. This method allowed measurement of the time change of the PWV at approximately the arrival
time of the pulse wave, which discriminates the period when the reﬂected component is not contaminated.
© 2018 The Japan Society of Applied Physics

1.

Introduction

The arterial wall consists of three layers: (1) the intima,
which is the innermost thin layer; (2) the thick media, whichcontains elastin, smooth muscle, and collagen; and (3) the
outermost adventitia, which is predominantly made of stiﬀ
collagenous ﬁbers. In the media, collagen is the stiﬀest wallconstituent with elastic moduli of 3–100 MPa.1) The elastic
moduli of elastin and smooth muscle are 6 × 102 and(0.1–2.5) × 102 kPa, respectively.2)
Clinical observations suggest that the ratio of nondistensible components (collagen and basement membrane) to thedistensible components (smooth muscle and elastin) changes
markedly with aging and the progression of atherosclerosis,
which structurally aﬀects the elastic behavior of the arterial
wall.3,4) In particular, in the early stage of atherosclerosis, thecholesterol ester content of the aortae signiﬁcantly aﬀects the
dynamic Young’s modulus of the aorta.5)
The elasticity or viscoelasticity of the arterial wall has beenmeasured in extracted blood vessels or exposed vessels inanimal experiments.2,6–12) Alternatively, changes in the stiﬀness of human arteries can be assessed by the noninvasive
measurement of displacement of the arterial wall using an
ultrasonic phase-locked echo tracking system.13,14) However,in those studies, the pulse pressure, which is essential for
viscoelasticity estimation, was measured at the brachial artery.
As a noninvasive clinical method for evaluating arterial
elasticity, pulse wave velocity (PWV) has been used for the
diagnosis of arteriosclerosis for more than 100 years.15–17) On
the basis of wave transmission theories, PWV is determinedusing the well-known Moens–Korteweg formula:sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
E h
PWV ¼
;
ð1Þ
2r0
where Eθ is the Young’s modulus of elasticity in thecircumferential direction of the arterial wall, r0 and h are
the internal radius and thickness of the arterial vessel,
respectively, and ρ is the density of blood. The assumptions
for the Moens–Korteweg equation are that the artery has athin wall (i.e., h=2r0 is suﬃciently small) and is ﬁlled with anincompressible inviscid liquid. From the noninvasive meas-

urement of the PWV in Eq. (1), the elasticity of the arterial
wall is evaluated.
More exact solutions of pulse wave transmission havealso been reported.15,18,19) The full correction equation was
described by Bergel,2,6) and its eﬀective simpliﬁcation issﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
1E hPWVðE Þ ¼
;
ð2Þ

2
1   2r0
where σ is the Poisson’s ratio of the arterial wall. Using a
Poisson’s ratio of 0.5 results in a derived velocity PWV(Epﬃﬃﬃﬃﬃﬃﬃﬃ θ)that is higher than the PWV in Eq. (1) by a factor of 4=3 
1:15. Noninvasive evaluation of PWV from the elastic
modulus Eθ uses the Moens–Korteweg equation shown in
Eq. (1) or (2); the latter is more accurate when theviscoelastic eﬀects are included.20)
In numerous studies, various methods have been developed for measuring the PWV of extracted or exposed arteries
in anesthetized animals. These are divided into the following
four categories.
1. Wave-front velocity measurement using a pair ofcatheter-tip manometers21) or the systolic foot-to-footvelocity measurement using pressure pulses by in vivo
aortic catheterization.8) For the exposed arteries, thephase velocity of the harmonic components of small
artiﬁcially generated pressure waves was measured bothin the downstream and upstream directions.22,23)
2. Estimation of the PWV in Eq. (1) based on themeasurement of the dynamic elastic modulus detectedfrom the oscillatory stress–strain relationships at eachfrequency.6,8,12)
3. Frequency-dependent phase velocity determinationfrom the propagation constant (γ) based on the theoryof transmission lines using the Fourier spectra ofmeasured pressure and blood ﬂow, or pressures
measured at three or four points in an arterial segment
where forward and reﬂected waves exist.24–35) Complex
characteristic impedance and local reﬂection coeﬃcientswere also determined.36–41)
4. The phase velocities in the artery were calculated fromthe Fourier spectra of simultaneous measurements ofpressure at two sites.42,43)

07LF14-1© 2018 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 57, 07LF14 (2018)

M. Ito et al.

All of these methods were applied to extracted arteriesin vitro, or exposed or unexposed arteries of anesthetizedanimals or patients in vivo using invasive manometers.
Alternatively, some noninvasive methods of in vivo
measurement of PWV have been developed, including theassessment of foot-to-foot velocity from a pair of pressure
waves measured on the skin surface,44–46) from a pair ofdisplacement components,47–50) or from velocity components51,52) in the radial direction of the arterial wall using
two-channel echo tracking devices, or from blood ﬂow speed
at two points using ultrasound.53–57) In all of these noninvasive methods, the pressure wave near the skin surface,wall displacement, wall velocity, blood ﬂow, and radiatedsound are measured at two points along the vessel wall, andthe delay time in the transmission of the foot of pulse
waveforms (i.e., the point showing the sharpest change inthe wave) is determined. PWV is determined only at the
beginning of the ejection period TE.
However, to the best of our knowledge, there are noreports of measurement of PWV at periods other than TE
during one cardiac cycle. As described above, as the arterial
wall exhibits nonlinear characteristics in the stress–strain
relationship, PWV changes during one cardiac cycle becauseof the change in inner pressure. Furthermore, the velocity
dispersion in PWV in vivo has not been reported. The
measurable frequency of typical PWV components is lessthan 20 Hz. Thus, the wavelength at 20 Hz is approximately
25–50 cm, as typical PWVs in humans are approximately
5–10 m=s. In the presence of both a forward transmission
wave and a backward reﬂection wave, these two components
cannot be separated in the time domain. At the beginning of
the ejection period TE, only the forward transmission wave
exists. Thus, PWV is only measured noninvasively at thistime.
In conventional measurement methods, blood pressure ismeasured at two points. PWV is calculated from thediﬀerence in the rise time of blood pressure waveforms andthe distance between two points, as in the case of the carotidfemoral PWV method,47,58) by which PWV is calculated fromthe carotid artery to the femoral artery, and the brachial-ankle
PWV method, by which PWV is calculated between thebrachial artery and the ankle. However, these methods havethe following problems.
1. The measurement region is as wide as several tens ofcentimeters, such as between the carotid artery and thefemoral artery or between the brachial artery and theankle. Although PWV increases as much as inperipheral blood vessels,59) this eﬀect is not consideredin PWV measurements using conventional methods,
but PWV is rather calculated from the average velocity
over a wide region (from the central artery to peripheral
blood vessels).
2. The pulse wave generated with the heart beat propagates
toward the periphery of the arterial wall and is reﬂected
at vascular bifurcations and peripheral vessels.60)
Nevertheless, PWV is calculated on the assumptionthat the pulse wave has only an incident component.
Therefore, local lesions on the order of several millimeters
to tens of millimeters may not be evaluated correctly.61,62)
Moreover, Young’s modulus increases as arteriosclerosis
progresses, while PWV increases in proportion to the squareroot of Young’s modulus. As arteriosclerosis progresses, thepulse wave reﬂected from the peripheral bifurcations returns
earlier. Thus, the incident component of the pulse wave
interferes with the reﬂected component.
We previously reported the local PWV calculation method
using high-frame-rate ultrasound for in vivo measurementof the carotid artery.63) However, PWV was calculated onlyat the peak time of the acceleration waveforms of small
vibrations on the arterial wall, and the reﬂected pulse wave
was not observed in all subjects. In this study, we
noninvasively measured the velocity waveforms of small
vibrations at multiple points on the arterial wall using
ultrasound, and calculated the change in time of local PWV
by analyzing the phase waveforms of the velocity signals. By
calculating the change in time of the local PWV, the incident
and reﬂected components of the pulse wave were observed,
and the period including only the incident component of thepulse wave and that including only the reﬂected componentof the pulse wave were separately extracted for all subjects.
Moreover, the propagation of mechanical vibration accompanying the opening of the aortic valve was observed.
2.

Experimental methods

2.1 Tracking of the arterial wall using the phasedtracking method

In this study, we measured small vibrations on the arterial
wall as velocity waveforms using the phased-tracking
method.64,65) In this method, the average velocity during
the pulse transmission interval ΔT is obtained as the
waveform v(t) from the phase diﬀerence ðx; tÞ during theperiod ΔT as follows:


T
xðtÞ
ðx; tÞ
¼ c0 
v^ t þ
;ð3Þ
¼
2
T
4f0 T
where c0 is the velocity of the ultrasound, Δx(t) is thedisplacement of an object during the period ΔT, and f0 is thefrequency of the ultrasound.
2.2 Calculation of PWV by the least squares method
The analytic signal a(n) of the velocity waveform v(n) in
Eq. (3) on the arterial wall was calculated using the Hilberttransform, where n is a frame number. The phase waveformθ(n) of the analytic signal a(n) was discontinuous because
the range of the phase θ(n) was −π < θ(n) ≤ π. To obtain
continuous waveforms, the phase unwrapping process wasapplied. Then, the line with similar phase values from the ﬁrst
beam to the last beam was determined by the least squares
method to estimate the component that propagates with PWV
as follows. First, when we assume a value of PWV, the arrival
time tm,n,PWV of the pulse wave on the mth ultrasound beam isgiven bytm;n;PWV ¼

d  mþ T  n ðm ¼ 0; 1; . . . ; MÞ;
PWV

ð4Þ

where Δd is the interval beams, ΔT is the sampling intervalof the velocity waveform v(t), and ΔT · n is the base time seton the 0th beam of the selected nth frame. The instantaneous
phase value θm(tm,n,PWV) at the time tm,n,PWV for the mth beamobtained from the analytic signal is described above.
Second, the pulse wave velocity PWV(ΔT · n) at a time
ΔT · n is determined by minimizing the following root of thevariance, ðPWV; nÞ, of θm(tm,n+k,PWV) along the straight line

07LF14-2© 2018 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 57, 07LF14 (2018)

M. Ito et al.
32 mm

32 mm
5 mm

beam 0beam 1beam 10Anterior wall.......

Pulse wave

Heart side

Vascular lumen

Head side

initial setting points at thetime of the Q wave of the
ECG for the following
tracking processing

Posterior wallFig. 1. (Color online) Schematic diagram of the in vivo measurement.

determined by Eq. (4) in all beams (m ¼ 0; 1; . . . ; M) related
to ΔT · n:
!
1
M
1X
1 X
2
ðPWV; nÞ ¼
jm ðtm;nþk;PWV Þ  k j ; ð5Þ
3 k¼1 M þ 1 m¼0
ECG

Fig. 2. (Color online) B-mode of subject A.

ð6Þand (M + 1) shows the number of ultrasound beams.
Experimental setting
In vivo measurements were performed using an ultrasonicdiagnostic device (Hitachi-Aloka ProSound F75) with a
6.0 MHz linear probe (Hitachi-Aloka UST-5415). Radio
frequency signals were acquired in the carotid artery of threehealthy male subjects (A, B, and C). The sampling frequency
was 40 MHz, and the resolution in the axial direction was
38.5 µm. The 11 ultrasound beams (beam number m ¼
0; 1; . . . ; 10) were set in the longitudinal direction along thearterial wall with intervals of Δd = 3.2 mm, and the velocity
waveform of a small vibration for each beam was measured
at the boundary between the media and the adventitia on theposterior wall of the carotid artery for 4 s. The frame rate was
1=ΔT = 521 Hz. The phase components θ(n) were interpolated in advance by the sinc function at seven points between
the sampling interval of ΔT. Figure 1 shows a schematic
diagram of the in vivo measurement.

Head side

2.3

3.
3.1

Results and discussion

Results of subject A
Figure 2 shows the B-mode image of subject A (23-year-old
healthy male). Figure 3 shows the velocity waveforms ofsmall vibrations on the arterial wall, which were obtained on
six beams {vm(t)} (m ¼ 0; 2; 4; 6; 8; 10). All velocity waveforms {vm(t)} showed two negative peaks immediately after
aortic valve opening, and two positive peaks immediately
after aortic valve closing. First, we focused on the time whenthe velocity waveforms of the small vibrations peaked oneach beam. When we assumed that the PWV was constantregardless of the measurement position, some pulse waves
were found to propagate, as shown by green lines,
immediately after the ﬁrst heart sound in the phonocardiogram (PCG); the incident and reﬂected components of thepulse wave were discriminated by the positive and negative
gradients of the lines, respectively. From the gradient ofeach green line, the velocities of the ﬁrst incident pulse wave

Head side

PCG

where k is the mean value deﬁned by
M
1 X
k ¼
m ðtm;nþk;PWV Þ;
M þ 1 m¼0…
Heart side

Beam No.

Aortic valve
opening

Aortic valve
closing

10velocity [mm/s]

8
6
4
2

3 mm/s0-5 mm/sHeart sidetime [s]Fig. 3. (Color online) Velocity waveforms of small vibrations on thearterial wall for even beams (m ¼ 0; 2; 4; 6; 8; 10), ECG, and PCG of subject
A.

and the second reﬂected pulse wave were 5.3 and −8.0 m=s,respectively.
The analytic signals of velocity waveforms were obtainedusing the Hilbert transform, and phase unwrapping wasapplied to the phase waveforms of the analytic signals to
obtain continuous phase waveforms. Figure 4 shows thecolor maps of the phase before and after the phaseunwrapping and the electrocardiogram (ECG) and PCG.
Figure 5(e) shows the PWV determined by applying the leastsquares method for Eq. (4) to the period immediately after
the ﬁrst heart sound. We considered that there was almost
no vibration on the arterial wall during the period when theroot mean square (RMS) of velocity was less than 1 mm=s.
Thus, we determined PWV until 0.25 s after the R-waveof the ECG, and focused on the time immediately after theﬁrst heart sound. At the time when the velocity waveformsof the small vibrations on the arterial wall had two peaks
immediately after the ﬁrst heart sound, the incident
component of the pulse wave was calculated as approx-

07LF14-3© 2018 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 57, 07LF14 (2018)velocity[mm/s]

(b)

−

(c)

longitudinal distance [mm]

(d)

(d)

−

[rad]

(e)

longitudinal distance [mm]propagation velocity [m/s](e)relative change RMS of velocity
in diameter [mm][mm/s] velocity [mm/s](c)phase [rad]

(b)

PCG

PCG

ECG

(a)

ECG

(a)

M. Ito et al.

[rad]

III
I

II

1 rad

time [s]time [s]Fig. 4. (Color online) Result of the phase unwrapping of subject A.
(a) ECG and PCG. (b) Velocity waveforms of small vibrations on the arterial
wall of beam 0 and beam 10. (c) Phase waveforms of the velocity of beam 0
and beam 10. (d) Color map of phase before the phase unwrapping. (e) Colormap of phase after the phase unwrapping.

imately 5.0 m=s at around 0.10 s, and the reﬂected componentof the pulse wave was calculated as approximately −8.0 m=s
at around 0.14 s. These results correspond to those shownin Fig. 3.
Moreover, a component of approximately 10 m=s was
obtained at 0.08 s immediately before the arrival of theincident component of the pulse wave, which is related tothe propagation of mechanical vibration accompanied by the
opening of the aortic valve as follows. Since the distancefrom the heart to the common carotid artery was roughly
17.5 cm, the times at which the mechanical vibration at 10m=s and the incident component of the pulse wave at 5.0 m=soccurred were calculated as 62.5 and 63.0 ms after the Rwave of the ECG, respectively. As shown by the broken anddotted lines in Fig. 5(a), the PCG showed a large peak at thetime when these two propagation components occurred.
Thus, these phenomena show that the pulse wave starts to
propagate with the opening of the aortic valve from the heart
to the common carotid artery by accompanying the mechanical vibration. By comparing the results at three heartbeats
shown in Fig. 5(e), the velocities estimated were similar for
the incident component of the pulse wave and the mechanicalvibration, while those for the reﬂected component of thepulse wave were diﬀerent.
The rise time of the relative change in the inner diameterof the blood vessel in Fig. 5(d), at which the PWV wasmeasured using the conventional method, corresponded tothe time at which the propagation component was converted
from the mechanical vibration to the incident component of
the pulse wave. Thus, the PWV at the rise time of the relative

Fig. 5. (Color online) (a) ECG and PCG of subject A. (b) Velocity
waveforms of small vibrations on the arterial wall of beam 0 and beam 10.
(c) RMS of velocity waveforms small vibrations on the arterial wall ofbeam 0 and beam 10. (d) Relative changes in the inner diameter of the bloodvessel. (e) Pulse wave velocity of subject A determined by the least squares
method.

change in the inner diameter of the blood vessel waveform(approximately 8.0 m=s) in Fig. 5(d) was slightly higher thanthat of the incident component of the pulse wave. By theconventional technique, the risk of arteriosclerosis isconsidered high if the PWV is ≥14 m=s measured by thebrachial-ankle PWV method,66) or if the PWV is ≥10 m=smeasured by the carotid-femoral PWV method.67) The
velocity of the incident pulse wave component estimated in
the present study was within the normal range based on these
diagnostic criteria.
3.2 Results of subject B
Figure 6 shows the velocity waveforms that were obtained on
six beams of subject B (23-year-old healthy male). The
velocities of the ﬁrst incident pulse wave and the second
reﬂected pulse wave were obtained at 5.3 and −10.7 m=s,respectively. At the same time, the incident and reﬂectedcomponents of the pulse wave were calculated by the leastsquares method as approximately 5.7 m=s around 0.14 s and−11 m=s around 0.17 s, respectively, in Fig. 7(e). These
results also corresponded to the results in Fig. 6. A
component of the mechanical vibration was observed as
approximately 10 m=s at around 0.13 s. Since the distancefrom the heart to the common carotid artery was roughly
17.5 cm, the times at which the mechanical vibration at 10m=s and the incident component of the pulse wave at 5.7 m=soccurred were calculated as 110 and 109 ms after the R-waveof the ECG, respectively. As shown by the broken and dotted

07LF14-4© 2018 The Japan Society of Applied Physics

M. Ito et al.

PCG

PCG

ECG

ECG

Jpn. J. Appl. Phys. 57, 07LF14 (2018)

Aortic valve
openingHead side

Aortic valve
closing

Beam No.

10

10

8

8
velocity [mm/s]

velocity [mm/s]

Head side
Beam No.

6423 mm/s-4 mm/s-6 mm/s0Heart sidetime [s]Heart side

Fig. 6. (Color online) Velocity waveforms of small vibrations on thearterial wall for even beams (m ¼ 0; 2; 4; 6; 8; 10), ECG, and PCG ofsubject B.

ECG
PCG

(d)

(e)
propagation velocity [m/s]time [s]Fig. 8. (Color online) Velocity waveforms of small vibrations on thearterial wall for even beams (m ¼ 0; 2; 4; 6; 8; 10), ECG, and PCG ofsubject C.

relative change RMS of velocity
in diameter [mm][mm/s] velocity [mm/s]

(c)

4

2
0

(b)

Aortic valve
closing

6

2 mm/s(a)

Aortic valve
opening

III
I II

1 rad
time [s]Fig. 7. (Color online) (a) ECG and PCG of subject B. (b) Velocity
waveforms of small vibrations on the arterial wall of beam 0 and beam 10.
(c) RMS of velocity waveforms of small vibrations on the arterial wall ofbeam 0 and beam 10. (d) Relative changes in the inner diameter of the bloodvessel. (e) Pulse wave velocity of subject B determined by the least squares
method.

lines in Fig. 7(a), the PCG showed a peak at the time whenthese two propagation components occurred. By comparing
the results between two heartbeats as shown in Fig. 7(e), thevelocities estimated were similar for the incident componentof the pulse wave and the mechanical vibration, while thosefor the reﬂected component of the pulse wave were diﬀerent.

The rise time of the relative change in the inner diameter ofthe blood vessel in Fig. 7(d) also corresponded to the time atwhich the propagation component was converted from themechanical vibration to the incident component of the pulse
wave, while the PWV at that time was slightly higher than theincident component of the pulse wave. On the basis of thediagnostic criteria of the conventional methods, the velocityof the incident pulse wave component estimated in thepresent study was within the normal range.
3.3 Results of subject C
Figure 8 shows the velocity waveforms that were obtainedon six beams of subject C (24-year-old healthy male). The
velocities of the ﬁrst incident pulse wave and second reﬂected
pulse wave were 5.6 and −7.1 m=s, respectively. At the sametime, the incident and reﬂected components of the pulse wave
were calculated by the least squares method as approximately
5.7 m=s at around 0.11 s and approximately −7.0 m=s ataround 0.14 s, respectively, in Fig. 9(e). These results also
corresponded to the results in Fig. 8. A component of themechanical vibration was observed as approximately 10 m=s
at around 0.10 s. Since the distance from the heart to thecommon carotid artery was roughly 17.5 cm, the times atwhich the mechanical vibration at 10 m=s and the incident
component of the pulse wave at 5.7 m=s occurred were
calculated as 78.5 and 79.2 ms after the R-wave of the ECG,
respectively. As shown by the broken and dotted lines inFig. 9(a), the PCG showed a peak at the time when thesetwo propagation components occurred. By comparing theresults among three heartbeats as shown in Fig. 9(e), thevelocities estimated were similar for the incident componentof the pulse wave and the mechanical vibration, and those forthe reﬂected component of the pulse wave were also similar,
which was diﬀerent from those of subjects A and B; thereason is considered below.
The rise time of the relative change in the inner diameterof the blood vessel in Fig. 9(d) also corresponded to the timeat which the propagation component was converted from themechanical vibration to the incident component of the pulse
wave. On the basis of the diagnostic criteria of the conventional methods, the velocity of the incident pulse wave

07LF14-5© 2018 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 57, 07LF14 (2018)[rad]Fig. 10. (Color online) Phase waveforms of each beam and diﬀerence
between the maximum phase value and the minimum phase value forsubject A.
occurrence ofpulse wave

relative change
in diameter [mm](d)time[s]propagation velocity [m/s]

(e)

III

incident componentof pulse wave

I II

1 rad
time [s]Fig. 9. (Color online) (a) ECG and PCG of subject C. (b) Velocity
waveforms of small vibrations on the arterial wall of beam 0 and beam 10.
(c) RMS of velocity waveforms of small vibrations on the arterial wall ofbeam 0 and beam 10. (d) Relative changes in the inner diameter of the bloodvessel. (e) Pulse wave velocity of subject C determined by the least squares
method.

component estimated in this study was within the normal
range.
3.4 Comparison between subjects
As shown in Figs. 5(e), 7(e), and 9(e), the three propagation
components, namely, the mechanical vibration and theincident and reﬂected components of the pulse wave wereobserved in all subjects immediately after the ﬁrst heartsound. Therefore, the existence of these three components
does not depend on the subjects. By comparing the results
among heartbeats, the velocities estimated were similar for
the incident component of the pulse wave and the mechanicalvibration for the three subjects, while those for the reﬂectedcomponent of the pulse wave were diﬀerent for subjects A
and B. The reason is considered as follows. The maximum
diﬀerences between the phase values in all beams were large
for the period during which the incident components of thepulse wave were observed. On the other hand, for the period
when the reﬂected components were observed, the maximum
diﬀerences between the phase values were small. As an
example, Fig. 10 shows the phase waveforms on all beams
and the maximum diﬀerences between the phase values in all
beams in the ﬁrst heartbeat of subject A. The maximum
diﬀerences between phase values at around 0.10 s when theincident component of the pulse wave was observed werelarger than those at around 0.14 s during the period which thereﬂected component of the pulse wave was observed. Since
the phase values of all beams were similar for the period

propagation velocity [m/s](c)relative change RMS of velocity
in diameter [mm][mm/s] velocity [mm/s](b)phase [rad]

PCG

ECG

(a)

M. Ito et al.

interference

mechanicalvibrationreflected componentof pulse wave

5 ms

III
0

80-130 ms
from R wave

10-20 ms
0.15

0.1

I

II

time from R waveof ECG [s]5- 10-30
10 ms
ms

Fig. 11. (Color online) Illustration explaining the three periods of thetypical propagation components.

Table I. Root of the variance MIN ðPWV; nÞ of the phase in thedetermination of PWV (in deg).
Subject

Period I

Period II

Period IIIA
B

1.26–3.90
1.15–2.81

3.67–9.17
2.75–4.81

1.66–2.29
0.92–1.20

C

1.20–2.64

2.58–3.84

0.63–1.20

when the reﬂected components were observed, the changein MIN ðPWV; nÞ with PWV was small and it was diﬃcult
to calculate PWV accurately. Thus, the velocities of thereﬂected component of the pulse wave were diﬀerent among
heartbeats.
As illustrated in Fig. 11, the propagation components weredivided into three periods for all the subjects. Period I is theperiod from the rise time of the inner diameter of the bloodvessel to the time when the temporal change in propagation
velocity has discontinuity of approximately 3 m=s. Period II
is the period from the end of period I to the time when the
propagation velocity changes from positive to negative.
Period III is the period after the time when the propagation
velocity became negative. The error bars of PWV observedin Figs. 5(e), 7(e), and 9(e) show the root of the variance inthe determination of speed in Eq. (5), and Table I shows theroot of the variance ðPWV; nÞ for each period for the threesubjects. In all the three subjects, the values of the root of thevariance ðPWV; nÞ in period II were larger than those in

07LF14-6© 2018 The Japan Society of Applied Physics

M. Ito et al.

velocity of the reflected component of the pulse wave [m/s]Jpn. J. Appl. Phys. 57, 07LF14 (2018)

the three subjects, the three propagation components, namely,
the mechanical vibration and the incident and reﬂectedcomponents of the pulse wave, were obtained immediately
after the ﬁrst heart sound. Furthermore, the reﬂectedcomponent of the pulse wave was calculated as faster than
the incident component in all subjects. By the conventional
method, PWV can only be calculated at a characteristic time,such as at the rise time of blood pressure waveforms.59) By
contrast, using our proposed method, it is possible tocalculate the change in time of the local PWV at every timefor every phase, by using the phase of analytic signals. Thus,
this method may be useful for a more accurate assessment oflocal arteriosclerosis.
velocity of the incident component of the pulse wave [m/s]41)

A. C. Burton, Physiol. Rev. 34, 619 (1954).
D. H. Bergel, J. Physiol. 156, 445 (1961).
T. Hirai, S. Sasayama, T. Kawasaki, and S. Yagi, Circulation 80, 78 (1989).
M. A. Hajdu, D. D. Heistad, J. E. Siems, and G. L. Baumbach, Circ. Res.
66, 1747 (1990).
T. I. Pynadath and D. P. Mukherjee, Atherosclerosis 26, 311 (1977).
D. H. Bergel, J. Physiol. 156, 458 (1961).
J. A. M. Hinke and M. L. Wilson, Am. J. Physiol. 203, 1153 (1962).
B. M. Learoyd and M. G. Taylor, Circ. Res. 18, 278 (1966).
D. J. Patel, W. K. Tucker, and J. S. Janicki, J. Appl. Physiol. 28, 578 (1970).
D. H. Bergel, in Biomechanics, ed. Y. C. Fung (Prentice-Hall, Englewood
Cliﬀs, NJ, 1972).
D. J. Patel, J. S. Janicki, R. N. Vaishnav, and J. T. Young, Circ. Res. 32, 93(1973).
R. H. Cox, Am. J. Physiol. 229, 1371 (1975).
D. J. Mozersky, D. S. Sumner, D. E. Hokanson, and D. E. Strandness, Jr.,
Circulation 46, 948 (1972).
T. Kawasaki, S. Sasayama, S. Yagi, T. Asakawa, and T. Hirai, Cardiovasc.
Res. 21, 678 (1987).
J. C. Bramwell and A. V. Hill, Proc. R. Biol. Sci. B 93, 298 (1922).
J. C. Bramwell, A. V. Hill, and B. A. McSwiney, Heart 10, 233 (1923).
P. Hallock, Arch. Int. Med. 54, 770 (1934).
J. R. Womersley, J. Physiol. 127, 553 (1955).
G. W. Morgan and W. R. Ferrante, J. Acoust. Soc. Am. 27, 715 (1955).
W. W. Nichols and M. F. O’Rourke, McDonald’s Blood Flow in Arteries.
Theoretical, Experimental and Clinical Principles (Edward Arnold,
London, 1998) 4th ed.
D. A. McDonald, J. Appl. Physiol. 24, 73 (1968).
M. Anliker, M. B. Histand, and E. Ogden, Circ. Res. 23, 539 (1968).
M. B. Hisland and M. Anliker, Circ. Res. 32, 524 (1973).
M. G. Taylor, Phys. Med. Biol. 1, 258 (1957).
U. Gessner and D. H. Bergel, IEEE Trans. Biomed. Eng. BME-13, 2(1966).
D. A. McDonald and U. Gessner, in Hemorheology, ed. A. L. Copley(Pergamon, Oxford, U.K., 1968) p. 113.
R. H. Cox, J. Biomech. 3, 131 (1970).
R. H. Cox, Circ. Res. 29, 407 (1971).
N. Westerhof, P. Sipkema, G. C. Van den Bos, and G. Elzinga, Cardiovasc.
Res. 6, 648 (1972).
W. R. Milnor and W. W. Nichols, Circ. Res. 36, 631 (1975).
W. R. Milnor and C. D. Bertram, Circ. Res. 43, 870 (1978).
R. Busse, R. D. Bauer, A. Schabert, Y. Summa, and E. Wetterer, Circ. Res.
44, 630 (1979).
J. K.-J. Li, J. Melbin, K. Campbell, and A. Noordergraaf, J. Biomech. 13,1023 (1980).
J. K.-J. Li, J. Melbin, R. A. Riﬄe, and A. Noordergraaf, Circ. Res. 49, 442(1981).
R. D. Latham, N. Westerhof, P. Sipkema, B. J. Rubal, P. Reuderink, andJ. P. Murgo, Circulation 72, 1257 (1985).
C. J. Mills, I. T. Gabe, J. H. Gault, D. T. Mason, J. Ross, Jr., E. Braunwald,
and J. P. Shillingford, Cardiovasc. Res. 4, 405 (1970).
W. Sperling, R. D. Bauer, R. Busse, H. Körner, and Th. Pasch, Pﬂügers
Arch. Eur. J. Physiol. 355, 217 (1975).
A. P. Avolio, Med. Biol. Eng. Comput. 18, 709 (1980).
J. K. Li, J. Melbin, and A. Noordergraaf, Am. J. Physiol. 247, H95 (1984).
K. H. Parker, C. J. H. Jones, J. R. Dawson, and D. G. Gibson, Heart Vessels
4, 241 (1988).
C.-C. Lee and R. G. Mark, IEEE Trans. Biomed. Eng. 40, 833 (1993).

07LF14-7© 2018 The Japan Society of Applied Physics

Fig. 12. (Color online) Relationship of the velocity of the incident wave
component with the velocity of the reﬂected wave component of the threesubjects.

periods I and III. The reason is maybe the interference
between the incident component and the reﬂected componentof the pulse wave in period II. The degree of this interference
increases as the position becomes close to the origin of thereﬂection. Thus, the root of the variance ðPWV; nÞ became
large.
The relationship of the velocity between the incident
component and the reﬂected component for the three subjects
is shown in Fig. 12. The reﬂected components of the pulse
wave were calculated as faster than the incident components
in all subjects. This ﬁnding is related to arterial pressure. As
blood is ejected from the heart into the artery immediately
after the ﬁrst heart sound, the arterial pressure rises and theinner diameter of the blood vessel dilates [shown by the
relative change in the inner diameter of the blood vessel
waveforms in Figs. 5(d), 7(d), and 9(d)]. Thus, the innerdiameter of the blood vessel at the arrival time of the reﬂectedcomponent of the pulse wave was larger than that at thearrival time of the incident component of the pulse wave.
The modulus of elasticity of the arterial wall increases as
the inner diameter of blood vessel increases, and the PWV
increases. The arterial pressure at the arrival time of thereﬂected component of the pulse wave was higher than that at
the arrival time of the incident component of the pulse wave.
Thus, the PWV at the arrival time of the reﬂected component
was estimated to be higher.
The distance from the measurement point to the point at
which the pulse wave was reﬂected was calculated fromusing the velocities of the incident and reﬂected componentsof the pulse wave. The distances were approximately 10.6 cm
for subject A, 11.7 cm for subject B, and 10.4 cm for subject
C. From the estimated distance, the pulse wave would reﬂect
from the vascular bifurcations in the arterial circle of Willis,
which is at the base of the brain.

1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)

21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
36)

4.

Conclusions

37)

In this study, we measured the velocity of small vibrations on
the arterial wall in vivo using the phase-tracking method. We
applied phase unwrapping to the phase of analytic signals to
obtain continuous waveforms, and then calculated the change
in time of the local PWV by the least squares method. In all

38)
39)
40)

Jpn. J. Appl. Phys. 57, 07LF14 (2018)

M. Ito et al.

42) I. T. Gabe, J. Karnell, I. G. Porje, and B. Rudewald, Acta Physiol. Scand.
61, 73 (1964).
43) J. D. Bargainer, Circ. Res. 20, 630 (1967).
44) T. Hayashi, Tokyo Jikei Ikadaigaku Zasshi 85, 548 (1970) [in Japanese].
45) M. Hasegawa, Tokyo Jikei Ikadaigaku Zasshi 85, 742 (1970) [in Japanese].
46) S. Yoshimura, M. Hasegawa, Y. Yabe, C. Arai, Y. Kashiwakura, H.
Tanaka, T. Kawasaki, Y. Aizawa, M. Abe, C. Hayashi, T. Komazawa, K.
Nakayama, S. Yagi, and S. Kinoshita, Kokyu to Junkan 24, 376 (1976)[in Japanese].
47) T. Imura, K. Yamamoto, K. Kanamori, T. Mikami, and H. Yasuda,
Cardiovasc. Res. 20, 208 (1986).
48) E. D. Lehmann and R. G. Gosling, Lancet 338, 1075 (1991).
49) M. Benthin, P. Dahl, R. Ruzicka, and K. Lindstrom, Ultrasound Med. Biol.
17, 461 (1991).
50) P. J. Brands, J. M. Willigers, L. A. F. Ledoux, R. S. Reneman, and A. P. G.
Hoeks, Ultrasound Med. Biol. 24, 1325 (1998).
51) H. Kanai, K. Kawabe, M. Takano, R. Murata, N. Chubachi, and Y. Koiwa,
Electron. Lett. 30, 534 (1994).
52) N. Chubachi, H. Kanai, R. Murata, and Y. Koiwa, Proc. IEEE Ultrasonics
Symp., 1994, PB-9, p. 1747.
53) A. P. Avolio, S.-G. Chen, R.-P. Wang, C.-L. Zhang, M.-F. Li, and M. F.
O’Rourke, Circulation 68, 50 (1983).
54) E. D. Lehmann, R. G. Gosling, B.-F. Langroudi, and M. G. Taylor,
J. Biomed. Eng. 14, 250 (1992).
55) E. D. Lehmann, K. D. Hopkins, and R. G. Gosling, Ultrasound Med. Biol.

19, 683 (1993).
56) K. Takazawa, N. Tanaka, K. Takeda, F. Kurosu, and C. Ibukiyama,
Hypertension 26, 520 (1995).
57) T. Nishiya, S. Senda, K. Katakura, M. Sugawara, M. Yuba, H. Morita, H.
Masugata, K. Yoshikawa, H. Yokoi, and H. Matsuo, Choonpa Igakukai 22,
695 (1995) [in Japanese].
58) S. Laurent, J. Cockcroft, L. Bortel, P. Boutouyrie, C. Giannattasio, D.
Hayoz, B. Pannier, C. Vlachopoulos, I. Wilkinson, and H. StruijkerBoudier, Eur. Heart J. 27, 2588 (2006).
59) D. A. McDonald, Blood Flow in Arteries (Edward Arnold, London, 1974).
60) M. Saito, Y. Yamamoto, Y. Shibayama, M. Matsukawa, Y. Watanabe, M.
Furuya, and T. Asada, Jpn. J. Appl. Phys. 50, 07HF10 (2011).
61) H. Hasegawa, M. Sato, and T. Irie, Jpn. J. Appl. Phys. 55, 07KF01 (2016).
62) Y. Miyachi, H. Hasegawa, and H. Kanai, Jpn. J. Appl. Phys. 54, 07HF18(2015).
63) H. Hasegawa, K. Hongo, and H. Kanai, J. Med. Ultrason. 40, 91 (2013).
64) H. Kanai, M. Sato, Y. Koiwa, and N. Chubachi, IEEE Trans. Ultrason.
Ferroelectr. Freq. Control 43, 791 (1996).
65) Y. Sakai, H. Taki, and H. Kanai, Jpn. J. Appl. Phys. 55, 07KF11 (2016).
66) A. Yamashina, H. Tomiyama, T. Arai, K. Hirose, Y. Koji, Y. Hirayama, Y.
Yamamoto, and S. Hori, Hypertension Res. 26, 615 (2003).
67) L. M. Van Bortel, S. Laurent, P. Boutouyrie, P. Chowienczyk, J. K.
Cruickshank, T. De Backer, J. Filipovsky, S. Huybrechts, F. U. MattaceRaso, A. D. Protogerou, G. Schillaci, P. Segers, S. Vermeersch, and T.
Weber, J. Hypertension 30, 445 (2012).

07LF14-8© 2018 The Japan Society of Applied Physics