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A new evaluation method for dependence of width of transmitted waves
on accuracy in multipoint simultaneous ultrasonic measurements ofcardiac wall vibration waveform
To cite this article: Naoya Furusawa et al 2019 Jpn. J. Appl. Phys. 58 SGGA08

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REGULAR PAPER

Japanese Journal of Applied Physics 58, SGGA08 (2019)https://doi.org/10.7567/1347-4065/ab1a30

A new evaluation method for dependence of width of transmitted waves on
accuracy in multipoint simultaneous ultrasonic measurements of cardiac wall
vibration waveform
Naoya Furusawa1, Shohei Mori2* , Mototaka Arakawa1,2 , and Hiroshi Kanai2,1
1

Graduate School of Biomedical Engineering, Tohoku University, Sendai, Miyagi 980-8579, Japan
Graduate School of Engineering, Tohoku University, Sendai, Miyagi 980-8579, Japan2*

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

Received November 9, 2018; accepted March 30, 2019; published online June 28, 2019
It has been revealed that the ultrasound measurement with high temporal resolution is useful for diagnosis of myocardial tissue properties.
However, it is considered that the dynamic measurement of the target tissue is affected by the motion of neighbor tissues because of the wide
width of the transmitted wave. For this reason, the measurement error is affected by spatial and temporal factors. In the present study, weconstructed an experimental system for measuring these effects quantitatively and investigated the accuracy of the velocity measurement using
some transmitted waves such as focused, plane, and diverging waves. In the conditions of the present study, the measurement error is minimized
at 9° of the angular width of the transmitted wave. This method is useful for evaluating the conditions of transmitted waves for measurements ofother targets which need a high temporal resolution such as shear wave, cardiac blood flow, and so on.
© 2019 The Japan Society of Applied Physics

1. Introduction

As ultrasound diagnosis is superior in a temporal resolution
and suitable for repetitive application, it has been widely
applied to measurements in the living body such as elastography on the heart or artery wall,1–3) blood ﬂow in theheart,4–7) visualization of the shear wave,8,9) measurementof propagation of contraction or electrical signal on
myocardium,10–14) and so on. The experimental environment
to be simulated is decided by the speciﬁc measurement target
from the above measurements. If it is possible to determine
the transmission condition that minimizes the measurement
error for the measurement object whose true value is known,
it is expected that the optimum measurement condition canalso be shown even in the in vivo experiment where the true
value is unknown.
Myocardial tissue functions can be evaluated by the
propagation speed of minute vibration velocity waveforms
within the maximum velocity of 60 mm s−1 on the heart wallacquired with high-frame-rate imaging using sparsely transmitted focused waves.15–17) As the other technique toimprove the temporal resolution, it had been proposed thatan unfocused wave is transmitted and multiple focusedreceiving beams are created from received signals by pluralelements of the ultrasonic probe.18–23) As this method
increases the spatial resolution by forming the received
beams with high density, it was applied to strain measurements at multiple points in the heart wall.24)
As mentioned above, a high temporal resolution is requiredfor dynamic measurements of the heart, so many researches
in cardiac ultrasound are focused on improving the temporal
resolution. However, by broadening the width of the transmitted wave spatially, the spatial resolution and signal-tonoise ratio (SNR) are, in general, degraded. Moreover, it isconsidered that the dynamic measurement of the target tissue
is affected by the motion of the neighbor tissues. Therefore,high spatial and temporal resolutions with high SNR areneeded for the dynamic measurement of the heart, while there
is a trade-off relationship among the temporal resolution,
the spatial resolution in the minute vibration velocity

measurement, and the SNR. The trade-off relationshipbetween the image quality and the frame rate has been
investigated using a static target.25) However, the measurement accuracy of the minute vibration velocity in a moving
target has not been investigated considering the trade-off
relationship among the temporal resolution, the spatial
resolution in the minute vibration velocity measurement,
and the SNR.
In a previous study, we constructed a basic experiment
system to evaluate the relationship between the condition oftransmitted waves and the accuracy of the minute vibration
velocity measurements.26) However, the evaluation method
for optimum condition of transmitted waves considering theabove trade-off relationship was not established. In addition,
the examined experimental conditions were insufﬁcient todetermine the optimum condition of transmitted waves forminute vibration velocity measurements.
In the present study, all transmitted wave conditions offocused, plane, and diverging waves were expressed uniformly by a single parameter, then we proposed an evaluation
method of the accuracy of the minute vibration velocity
measurement in each transmitted wave condition dependingon the above trade-off relationship. We constructed the basic
experimental system with setting several conditions tomeasure the minute vibration velocity waveform propagatingon the interventricular septum15) and demonstrated thequantitative evaluation of the accuracy of measuring theminute vibration velocity as a method for determining
the optimum condition of transmitted waves.
2. Methods
2.1. Evaluation method for measurement accuracy
considering trade-off relationshipIn the present study, we consider the measurement of thevibration waveform. Therefore, it is necessary to consider not
the mere spatial resolution but the spatial resolution of theminute vibration velocity measurement which means the
distance not to be affected by neighbor vibrations whose
velocity differs from the velocity of measurement target.
Then, we constructed an experimental system to investigate

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(a)

(b)

(c)

Fig. 2. (Color online) Deﬁnition of angular width θW of (a) focused wave,(b) plane wave, and (c) diverging wave.
Fig. 1. (Color online) Conﬁguration of the experimental system.

(a)the inﬂuence on accuracy of the vibration velocity measurement as shown in Fig. 1.
To evaluate the spatial resolution in the velocity measurement, two phantoms A and B were used as shown in Fig. 1.
The phantom B was set near the measurement target phantom
A as a neighbor vibration object whose velocity differs fromthe velocity of the measurement target. It is expected thatmeasurement error α increases by the inﬂuence of thereﬂected waves from phantom B when the diverging wave
is transmitted for the velocity measurement. The main
objective of this research is to evaluate the performance ofthe vibration measurement against the inﬂuence of thesurrounding vibrations under some transmission conditions,
so it is not desirable that the vibrations interfere with eachother on the phantom. Therefore, in the present paper, thetarget of the velocity measurement (phantom A) and aneighbor vibration object (phantom B) were spaced andindependently vibrated.
In this water tank experimental system, the vibration
velocity waveform v(U n ) of phantom A was measured byultrasound diagnosis equipment using a phased-tracking
method,27,28) and the vibration velocity waveform v L (n)was also measured by laser Doppler velocimetry as areference. To evaluate the accuracy of the vibration velocity,
the measurement error of the vibration waveform, α, wasdeﬁned as(b)Fig. 3. (Color online) The anticipation of measurement error of minutevibration velocity (a) without neighbor vibrations, (b) with neighborvibrations.

In the present study, we expanded the deﬁnition of theangular width q w to the focused wave to express alltransmitted wave conditions only by a single parameter q w.
The angular width q w was deﬁned as⎛ r - d⎞q w = 2 tan-1 ⎜w f⎟,
⎝ 2rf d ⎠N-1a=

å n = 0 {vU (n) - v L (n)}2
N-1

å n = 0 {v L (n)}2

,

(1 )

where N is the number of frames, and n is frame number.
Thus, the measurement accuracy of the velocity waveform
can be quantitatively evaluated with considering the trade-off
relationship among the temporal resolution, the spatial
resolution in the velocity measurement, and the SNR in thepresent experimental system.
2.2. Expression of transmitted wave conditions with asingle parameter
To express the condition of transmitted waves such as
focused, plane, and diverging waves, we deﬁned the angularwidth q w. The angular width q w was introduced in theprevious study to express the unfocused wave condition.2)(2 )where rf is depth of focal point, w is aperture width, and d istarget depth.
As shown in Fig. 2, rf of the focused wave is a positive
number (front side of the probe surface), and rf of thediverging wave is a negative number (virtual point source). In
the case of the plane wave, the focal point is at inﬁnity and q w
is 22° under the experimental condition. In the present study,
the focal depth of the transmitted wave with q w = 20° was
458 mm, which was thought to be far enough, it was dealt
with as a plane wave.
2.3. Anticipation of measurement error
We predict the measurement error α for measurements of theminute vibration velocity waveform propagating on theventricular septal wall as the schematic view shown in Fig. 3.

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Figure 3(a) shows the case where there is no neighbor object.
On the other hand, Fig. 3(b) shows the case where there is aneighbor object whose velocity differs from that of themeasurement target.
Each orange and gray line in Fig. 3 shows the measurement error α for the change of the angular width q w under thesame frame rate. In this case, it is expected that themeasurement error of the vibration velocity will decrease,since the SNR increases as the width of the transmitted wave
is narrower. The larger the q w is, the more gradual the changein SNR. Thus, the measurement error prediction curve in
Fig. 3(a) is considered to be convex upward for the change inangular width. On the other hand, in the case of Fig. 3(b), it isconsidered that the larger q w is affected by the surrounding
vibrations. Therefore, the measurement error prediction curveis considered to be downward convex.
In the phased-tracking method, the maximum velocity
measured without aliasing is determined by the frame rate in
the measurement. Therefore, when the velocity of an object
vibrating with various velocity components is measured by
the phased-tracking method, velocities higher than the upper
limit of the velocity cannot be accurately measured. As aresult, as the frame rate decreases, the measurement error
increases.
The minimum frame rate FRMIN required to avoid aliasing
is expressed as
FRMIN = ∣ v MAX ∣

4f0
,
c0

(3 )

where ∣ v MAX ∣ is the absolute value of maximum velocity, f0 is
the transmission frequency, and c0 is the sound velocity. The
anticipated errors of the vibration velocity measurement at
the lower limit frame rate FRMIN are shown by the red dottedlines in Fig. 3. Measurement errors at a frame rate larger thanthe lower limit of the frame rate are indicated by the redregion. The orange solid lines are located lower than the red
dotted line and have a sufﬁcient frame rate for the measurement of the vibration velocity. The gray solid line is locatedhigher than the dotted red line, so it has an insufﬁcient frame
rate for the measurement of the vibration velocity.
On the other hand, as the transmission beam width isnarrower, the range of the vibration measurement per one
transmission becomes narrower, so that the number oftransmissions required for one frame increases. As a result,assuming a certain range of sector scanning, the maximum
frame rate for the minute vibration velocity measurement
decreases. Figure 4 shows a sector scan with the scanning
angle of the transmitted beam Δθ and the measurement range
q0. In this condition, if the transmission direction is tilted
beyond the transmission beam width, a region where a highintensity transmission wave does not reach is generated. Inorder to avoid the generation of this area, we set the range of
Dq as Dq £ q w. Then, the reachable frame rate FRMAX ismaximum when Dq = q w, and it is determined by the beamwidth. The relationship between FRMAX and q w is expressed
as
FRMAX = fPRF ·

qw
.
q0

(4 )

The maximum frame rate is indicated by a blue dotted line,
and the measurable region is highlighted in blue in Fig. 3.

Fig. 4. (Color online) The scan by tilt angle Δθ and the angular range θ0 of
the ﬁeld of view.

Therefore, the region satisfying Eqs. (3) and (4) is effective
for the vibration velocity measurement.
Because q w is the angular width of the transmitted beam,
the reachable upper frame rate can be determined assuming
the sector scanning for cardiac measurement. However, in thecase where the object to be measured is a shear wave forelastography in such as the liver, muscle, breast, and so on,
the linear scan is used rather than the sector scan. Therefore,
in order to specify the reachable upper frame rate for the
linear scan, it is necessary to prepare another reasonable
expression to associate the frame rate and the beam width.
It is considered that q w [red point in Fig. 3(a)] at which theerror is the smallest in the case that there is neighborvibration is smaller than that in the case there is no neighborvibration [red point in Fig. 3(b)]. Therefore, q w at theminimum measurement error changes due to the inﬂuenceof the neighbor vibration.
2.4. Water tank experiments
The experimental system was introduced to observe theminute vibration velocity waveform caused by changes ofq w described in the previous section. The experimental
conﬁguration is shown in Fig. 1. RF data were acquired by
the ProSound-SSD α10 (Aloka) with a sector probe (UST52101N, Aloka) of 3.75 MHz of the transmission frequency.
The laser Doppler velocimetry (LV-1300, Ono Sokki) wasused as the reference. In the case of ultrasound measurement,
received beams were formed in the range of ±21° using RF
data acquired by one transmitted wave perpendicular to theprobe surface. Minute vibration velocity waveforms wereobtained from a center received beam (0°) using the phasedtracking method. Measurement errors α in Eq. (1)were calculated from the velocity waveform for 167 ms(5 wavelengths of 30 Hz).
The measurement of the propagation speed of the minutevibration velocity waveform on the heart wall caused by the
myocardial contraction enables evaluation of myocardium
function.15) For measuring the propagation speed of myocardial contraction on the intervascular septum avoiding theinﬂuence of aliasing, we decided a spatial measurement
interval without causing aliasing even at the shortest wavelength of propagation speed. In the previous study, thepropagation speeds of contraction during avascularization
condition and normal condition were approximately
1.6–3.6 m s−1. Propagations of contraction responses on the

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N. Furusawa et al.

intervascular septum were analyzed at 10–90 Hz where they
can be observed with high SNR.19,29) Here, the wavelength ofthe propagation wave was calculated as approximately
20 mm from the minimum velocity of 1.6 m s−1 and with afrequency of 80 Hz. Therefore, in the present study, twophantoms were spaced 10 mm corresponding to the half of
the wavelength to simulate the same movement on thephantom.
Phantom A, which is the measurement target, was vibrated
up and down with the sine wave at 30 Hz and the maximum
velocity of approximately 40 mm s−1 by a shaker A considering the minute vibration velocity waveform on theinterventricular septum.1) In the phased-tracking method, inorder to accurately measure the vibration at the maximum
velocity of 40 mm s−1, a frame rate of about 400 Hz isnecessary when the transmission frequency is 3.75 MHz. In
the present study, the velocity waveform was measured withframe rates of 1,683 Hz and 561 Hz to satisfy this condition.
A white noise was input to the shaker connected tophantom B to quantitatively evaluate the inﬂuence ofneighbor vibrations whose velocity differs from the measurement target. Although the frequency band of the input noise
can be changed freely, we chose the white noise as the input
noise for the demonstration experiment simulating thevelocity measurement with neighbor vibrations because it is
widely used as a background noise. The rms amplitude of thevelocity input to shaker B was set to be a half value comparedwith that of shaker A. Considering the depth of theinterventricular septum, two phantoms were set approximately 50 mm from the surface of the probe.
3. Results and discussion

Figure 5 shows B-mode images acquired by the transmitted
wave with an angular width of (a) q w = 9° (focused wave),(b) q w = 20° (plane wave) and (c) q w = 61° (diverging wave),respectively. As shown in Fig. 5(c), in the case of a diverging
wave, phantom A looked blurry which was caused by theeffect of a reﬂected wave from phantom B because of its wide
width of a transmitted wave.
Figure 6 shows an example of a waveform of the center
received beam in the depth direction used for the velocity
measurement. Large amplitudes were observed on the anterior and posterior surface of phantom A. The vibration
velocity at the anterior surface was analyzed.

(a)Fig. 6. An example of the waveform of the central receive beam.

Figure 7 shows the minute vibrated velocity waveforms
acquired by the transmitted wave with angular width of (a)q w = 9° (focused wave), (b) q w= 20° (plane wave) and (c)q w= 61° (diverging wave), respectively. Except for focused
waves of q w = 9, the amplitude of the velocity waveform
measured by the ultrasound tended to be larger than that ofthe velocity waveform measured by the laser Doppler
velocimetry. As the frame rate increased, the amplitude of
the velocity waveform measured by the ultrasound increased.
That also increased as q w increased.
Figure 8 shows measurement errors calculated by Eq. (1)on each transmitted wave condition. The blue dotted line
expresses the angular width of the ideal plane wave. In theseexperimental conditions, as the measurement error was
lowest at q w = 9, this transmitted wave condition was
evaluated as the best transmission condition among theparameters shown in Table I. In terms of the diverging
wave, the measurement errors in the case with phantom B
was larger than those in the case without phantom B.
Therefore, it was conﬁrmed that the inﬂuence of neighborvibrations increased as the beam width became wider.
Furthermore, in all graphs, the measurement error at
q w = 61° became larger than the measurement error at q w= 30°. It is considered that the increase of measurement error
was caused by the decrease of SNR with an increase of theangular width of the transmitted wave.
By contrast, the measurement error tended to decrease as
the frame rate was lower, contrary to the anticipation. This isbecause the effect of reverberation in the water tank might
increase as the frame rate became larger. This effect would be
reduced by attaching an ultrasonic absorption material to theinner wall of the water tank. If we can conﬁrm that the

(b)

(c)

Fig. 5. B-mode images acquired by (a) focused wave, (b) plane wave, and (c) diverging wave.

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(a)

(b)

(c)

Fig. 7. (Color online) The velocity waveform measured by (a) focused wave, (b) plane wave, and (c) diverging wave.

Fig. 8. (Color online) Angular width θW and the measurement error a ofvibration velocity.

Table I.
rf(mm)
θw(°)

80
9Transmission conditions.
107
12

458
20

−141
30

−26
61

measurement error increases as the frame rate decreases, thepredicted measurement error curve (blue dotted line shown in
Fig. 3) can be plotted from the measured values. Thus, it isconsidered that measurement conditions that minimize themeasurement error can be speciﬁed.
At q w = 12 and 20 in Fig. 8, the measurement errors
became larger than those with other angular widths, unlike
the anticipation in Fig. 3. We will investigate the cause
because the cause is unknown at the moment.
A deviation in the transmission frequency might beconsidered as a cause of the amplitude of the velocity
waveform not matching between the laser measurement andthe ultrasonic measurement even in the absence of phantom
B. When the transmission frequency adopted for the velocity

measurement in the phased-tracking method is deviated fromthe center frequency of the received waveform, the amplitudeof the estimated velocity waveform is affected. In order toeliminate this effect, a proper transmission frequency must be
determined to calculate the velocity waveform. This speciﬁcation method needs to be examined in the future.
The object of measurement in the present study is a minutevibration velocity waveform propagating on myocardium. In
the previous study,15–17) the minute vibration velocity waveform was calculated at plural points on the cardiac muscle,
and the propagation speed of these velocity waveforms wascalculated by the cross correlation between them. As a result,it was conﬁrmed that the propagation speed decreased in theischemic conditions. However, there were measurement
points where the correlation coefﬁcients between the vibration velocity waveforms were low, and the dispersion of theestimated propagation speed was large. Higher correlation isdesired in order to estimate the ischemic part more locally.
By examining the relationship between the correlation of theminute velocity waveforms and the measurement accuracy,
we believe that it is possible to specify the target value of themeasurement error for the minute velocity waveform in the
future.
If an acceptable measurement error can be speciﬁed
concretely and the measurement error indicated by thismethod cannot achieve the target value, it is necessary to
improve the beamforming method or the performance of
signal processing after imaging.30) Since the proposed
method can evaluate quantitatively the measurement accuracy of the vibration velocity, this method is also effective forthe evaluation of their performance.
In the case of a diverging wave, it was suggested that theartifact from phantom B interfered in the measurement ofvibration velocity of phantom A and this interference caused
an increase of measurement errors.

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In this study, vibration frequency and maximum vibration
velocity were selected as 30 Hz and 40 mm s−1, respectively.
On the other hand, in the case of a higher noise power
emitted by phantom B and shorter interval between two
phantoms, that of the wide transmitted wave would increase.
In the present study, we investigated some particular cases.
Therefore, there is a need for further investigation into
various situations. However, the proposed method and theexperimental system enables us to uniformly comparetransmission conditions and quantitatively to evaluate errorsof vibration velocity with variously changing measurement
conditions such as vibration velocity, noise power, anddistance between two phantoms. We have concluded that
future works can seemingly reveal the condition of theminimum measurement error.
The present evaluation method can determine the suitabletransmitted wave condition considering the trade-off relationship among the temporal resolution, the spatial resolution in
the velocity measurement, and the SNR. Although themeasurement target was set to the waveform of the minutevibration velocity on the heart wall in this paper, this method
is useful to optimize the transmitted wave conditions formeasurement of several targets which need a high temporal
resolution such as elastography,1–3) shear wave imaging,8,9)and so on.
If the object to be measured is the blood ﬂow in the heart,for example, by preparing a cardiac simulated phantom
driven by an internal pressure change, in place of the objectof the vibration measurement (phantom A) in this paper, it isconsidered that it is possible to decide a suitable transmission
condition for the blood ﬂow against the inﬂuence of neighborvibrations. In addition, if the object to be measured is a shear
wave, for example, by vibrating a part of the material close to
the viscoelasticity of the living body using this experimental
system, it is considered that it is possible to decide a suitabletransmission condition for the measurement of a shear wave
under the inﬂuence of neighbor vibrations.
4. Conclusions

For the determination of suitable transmitted wave conditionsof ultrasound in the measurement of the minute vibration
velocity waveform on the heart wall, we constructed anexperimental system and proposed a method to evaluate themeasurement accuracy considering the trade-off relationshipamong the temporal resolution, the spatial resolution in thevelocity measurement, and the SNR, in several conditions oftransmitted waves such as focused, plane, and diverging
waves. From the water tank experiment, we demonstrated thedetermination of the suitable transmitted wave condition formeasuring the minute vibration velocity waveform on theheart wall. The measurement errors of the vibration velocity
would systematically change depending on the experimental
conditions. Therefore, we will further investigate the errors invarious cases. Moreover, we will reveal how noises fromneighbor points affect the measurement accuracy. In the
future, we plan to limit the excitation frequency of thephantom B to the reasonable frequency band in in vivo.

Acknowledgments

This work was partially supported by JSPS KAKENHI Grant
No. 17H02105.
ORCID iDs

Shohei Mori https://orcid.org/0000-0002-5494-1055
Mototaka Arakawa
https://orcid.org/0000-0001-9386645X
Hiroshi Kanai https://orcid.org/0000-0002-6567-1687

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