Japanese Journal of Applied
Physics

BRIEF NOTE

Evaluation of error factors depending on ultrasonic transmitted
beamwidth in measurement of myocardial minute velocity
To cite this article: Kana Sugahara et al 2021 Jpn. J. Appl. Phys. 60 SDDE05

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BRIEF NOTEJapanese Journal of Applied Physics 60, SDDE05 (2021)
https://doi.org/10.35848/1347-4065/abef0e

Evaluation of error factors depending on ultrasonic transmitted beamwidth inmeasurement of myocardial minute velocity
Kana Sugahara1, Shohei Mori2*, Mototaka Arakawa1,2, and Hiroshi Kanai1,2
1Graduate 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 December 2, 2020; revised February 10, 2021; accepted March 16, 2021; published online April 1, 2021
A measurement by transmitting ultrasonic non-focusing beams increases the temporal resolution but causes an error in the velocity measurements
because of the lower signal-to-noise ratio (SNR) caused by the lower transmitted power and the lower spatial resolution. In the present study, weevaluated the relationship between the SNR and the transmitted beamwidth by the phantom experiment. The SNR decreased as the beamwidth
became wider, and the measurement error increased when SNR was lower than 10 dB. Furthermore, the error factor due to the low spatial
resolution more affected the measurement error than that due to the low transmitted power. © 2021 The Japan Society of Applied Physics

A diagnosis using echocardiography has the advantage ofnoninvasive and repetitive application compared with otherdiagnostic imaging methods. Ultrasonic measurement
methods for the evaluation of cardiac function such as thecharacterization of the heart,1) the visualizations of the bloodﬂow in the heart lumen,2–4) and the measurements of the
propagation of the contraction on the myocardium,5–9) havebeen studied.
As myocardium dynamics are fast and complicated, highresolution measurements are needed in both space and time
domains. One of the techniques for obtaining the hightemporal resolution in ultrasonic measurements is the methodthat an unfocused beam is sparsely transmitted and multiple
focused receiving beams are formed from the received
signals by the digital signal processing.7) However, ingeneral, broadening the beamwidth of the transmitted wave
causes the deterioration in the power of the transmitted wave
at the local region and the spatial resolution, and the velocity
measurement of the target medium is affected by the movements of neighboring tissues. Several methods have been
proposed to improve the signal-to-noise ratio (SNR) and thespatial resolution in the measurement using the unfocused
waves,10–16) and the beamforming performance has been
quantitatively evaluated for a static object to conﬁrm theusefulness of each method. Papadacci et al. quantitatively
evaluated the relationship between the beamwidth of thediverging wave and the spatially averaged SNR of the shear
wave velocity measurement.11) However, the relationshipbetween the transmitted beamwidth and the error of the
dynamic measurement has not been evaluated. The quantitative evaluation of the measurement accuracy in the dynamic
motion of the target object remains an issue.
Furusawa et al. proposed a method17) to determine theoptimal ultrasonic condition of transmitted beams for themeasurement of the cardiac dynamic motion.18) The experimental system was constructed simulating the measurementsof myocardial minute velocity, and the velocity estimation
accuracies with several conditions of the transmitted beam
were evaluated. However, the results were different as
expected because the measurement error by the focusedwave was larger than those by the plane and the diverging
waves in the same frame rate condition. It is difﬁcult to
conﬁrm the causes because the various error factors affected
the evaluation.

Thus, it is necessary to evaluate the effect of each error
factor independently. In our previous study, the effect ofvibration frequency was examined. It was conﬁrmed that theconstructed experimental system can evaluate the measurement error of the target velocity moved by the sine wave of
50 Hz with an accuracy of approximately 2%.19)
The measurement error of the myocardial velocity is
increased by the lower SNR, which is caused by the decreaseof the power of the transmitted wave arrived at a region ofinterest and the deterioration of the spatial resolution. In thepresent study, we quantitatively evaluated the relationshipamong the transmitted beamwidth, the lower SNR caused bybroadening the beamwidth, and the measurement error of theminute velocity. To evaluate each error factor, four types ofexperiments were conducted, (I) an experiment with nophantoms in a water tank, (II) an experiment with a target
phantom A, (III) an experiment with a noise source phantom
B, and (IV) an experiment with both of phantoms A and B.
The phantoms A and B were placed at the positions shown in
Fig. 1.
The measurement error was evaluated by comparing thevelocity waveforms measured by ultrasound with the reference velocity waveforms measured by the laser Doppler
velocimetry using the experimental system shown in Fig. 1.
The vibration of the urethane phantom A was measured byultrasound diagnosis equipment, and the velocity v
U (m ) was
obtained by applying the phased-tracking method20) to thecentral received beam. As the reference, the velocity v L (m )was measured by a laser Doppler velocimetry. The measurement error e 2 by the ultrasound was calculated as
M-1

e2 =

å m = 0 {vU (m) - v L (m)}2
åM-1{v L (m)}2
m=0

,

(1 )

where M is the number of samples in the velocity waveform.
We introduced the angular width q w to express the
beamwidth,17) which was deﬁned as⎛ r - d0 ⎞q w = 2 tan-1 ⎜w f⎟,
⎝ 2 rf d 0 ⎠(2 )where rf is the depth of focal point, w is the aperture width(19 mm), and d 0 is the target depth. The depth in Eq. (2) was
ﬁxed at 30 mm in the present study. The ﬁve different

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Jpn. J. Appl. Phys. 60, SDDE05 (2021)

K. Sugahara et al.

Fig. 1. (Color online) The schematic diagram of the experimental systemand the deﬁnition of the transmitted beamwidth.

transmitted beamwidths were used: focused waves(q w = 5 , 21), a plane wave (q w = 35), and diverging
waves (q w = 50, 65). The objective of the present study
was to evaluate the error factor caused by the lower power of
the transmitted signal and/or the lower spatial resolution, theframe rate in each measurement was ﬁxed at 3367 Hz which
was sufﬁciently high to measure the target velocity with avibration frequency of 50 Hz to avoid the error due to thetemporal resolution.
First, the velocity of the target phantom A was measured inexperiment (II) with only phantom A to evaluate only theerror factor of the lower power of the transmitted wave as thewider beamwidth. Then, the error factor concerned with thelower spatial resolution in addition to that of the lower
transmitted power was evaluated by measuring the velocityof the target phantom A in the experiment (IV) withphantoms A and B. The phantom B simulating a neighboring
tissue has a different velocity component compared with thetarget phantom A.
The SNR and the error of the velocity measurement were
calculated for 200 points in the range of depth d from 29.5 to33.5 mm near the surface of phantom A at several beamwidths and with or without the phantom B. The SNR was
calculated using Eq. (3) as SNRqw, d by the ratio of the signal
power from the measurement target A to the noise powerfrom the other sources.
K⎛ M-1
w · PS (d + k ) ⎞å1
k =-K k⎜⎟,
SNR q w, d = 10 log10
K
⎜M å
⎟
+
·
(
)
w
P
d
k
0
m
=
N
k
å
⎝
⎠

measured in the experiment (IV) with only the phantom B.
In all conditions, the power was calculated from the signal
obtained on the central received beam (red arrow in Fig. 1).
Radiofrequency data were acquired with a 7.5 MHz arrayprobe (UST-5412, ALOKA, Japan) and the ultrasounddiagnosis apparatus (Prosound α-10, ALOKA, Japan). The
sampling frequency was 40 MHz. The laser Doppler velocimetry (LV-1300, Ono Sokki, Japan) and the oscilloscope(TBS2104, Tektronix, U.S.A.) were used for measuring thereference velocity of the surface of the target phantom A.
For simulating the in vivo measurement, a surface of theurethan phantom A was placed at depth of 30 mm from theprobe surface and was vibrated up and down with a shaker
̈ & Kjær, Denmark). The vibration fre(Type 4810, Bruelquency was set at 50 Hz. The urethane phantom B was set
near the measured target phantom A as a neighboring tissue.
The velocity of the phantom B was set as 0 mm s−1 (i.e. thephantom B was not moved) to set the different velocity
compared with the measurement target phantom A.
The relationship among beamwidth, the measurement
error, and the SNRqw, d is shown in Fig. 2. In the experiment(II) using only the phantom A, there was a tendency that the
SNRqw, d decreased as the beamwidth broadened as shown in
Fig. 2(a). The measurement error was small at the
(a)

(b)

(3 )

(c)

k =-K

where M is the number of samples in the velocity waveform(673 points), K is the number of samples in the analysis
window (32 points), wk is the analysis window (Hanningwindow), and PS (d ) (or PN (d )) is the power of the received
signal at the depth d from the measurement target A (or theother sources). SNRqw, d related to the power of the transmitted
wave was calculated by the power of the signal, PS,A + water ,measured in the experiment (II) with only phantom A and by
the power of the noise, PN,water , measured in the experiment(I) with no phantoms in the water tank. SNRqw, d related toboth the power of the transmitted wave and the spatial
resolution was calculated by the power of the signal,
PS,A + water , measured in the experiment (II) with only
phantom A and by the power of the noise, PN,B + water ,Fig. 2. (Color online) The relationship among the transmitted beamwidth,
the measurement error of target velocity, and the SNRq w, d . (a) The
comparison between the experiment with the target phantom A, and theexperiment with the phantoms A and B, (b) the comparison among the ﬁve
beamwidths in the experiment with the phantom A, (c) the comparison
among the beamwidths in the experiment with the phantoms A and B.

SDDE05-2© 2021 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 60, SDDE05 (2021)
(a)

(b)

K. Sugahara et al.
(c)Fig. 3. (Color online) The M-mode images of the central received beam in
the experiment with (a) the phantom A, (b) the phantom B, and (c) thephantoms A and B. The red and blue lines were analysis range when SNRq w, d
was 21.5 dB.

measurement depth where SNRqw, d was higher than 10 dB andwas large at the depth where SNRqw, d was lower than 10 dB,
regardless of the beamwidth q w as Fig. 2(b). In the casewithout phantom B, there were no other scatterer or reﬂector
near the target phantom A and the frame rate was sufﬁciently
high to measure the velocity with the vibration frequency of
50 Hz. These results suggest that the increase of themeasurement error as the SNRqw, d lower in the experiment(II) without the phantom B is due to the lower PS,A + water , i.e.
lower power of the transmitted wave arrived at a local region
by broadening the ultrasound beamwidth.
In the experiment (IV) with both the target phantom A andthe neighboring phantom B, SNRqw, d was more decreased
compared with that without phantom B. On some measurement depths, the results showed the same relationshipbetween SNRqw, d and the measurement error, however, themeasurement errors exceeded 10% were obtained at themeasurement depths with higher SNRqw, d than 10 dB for
beamwidths more than 5°, which was not observed in theexperiment (II) without phantom B. In this case, the increaseof the measurement error was caused by both the lower
PS,A + water and the higher PN,B + water.
To discuss the difference of the relationship of SNRqw, d andthe measurement error between Figs. 2(b) and 2(c), the Mmode images were compared. Figure 3 shows the M-mode
images measured using the plane wave (q W = 35) for (a)only the phantom A [compatible with (II)], (b) only thephantom B [compatible with (III)], and (c) the phantoms A
and B [compatible with (IV)], respectively. In Fig. 3(c), theinterference pattern was observed at a depth deeper than
30.5 mm where the signal from phantom A in Fig. 3(a) andthe signal from phantom B in Fig. 3(b) overlapped. In theregion surrounded by red lines which includes interference
pattern, SNRqw, d was the same (21.5 dB) but the velocity
measurement error was 11.0% larger compared with thatsurrounded by the blue lines (measurement error: 2.3%)
which does not include the interference pattern. Thus, thevelocity measurement error increased by the interference of
scattered and/or reﬂected waves from the neighboring tissue
with different velocity even in the condition that themeasurement was less affected by the power of transmitted

signals. These results suggest that the error factor due to thelower spatial resolution more affected the measurement error
than that due to the lower power of the transmitted amplitude.
As the fundamental study, we quantitatively evaluatedeach error factor of the low transmitted power and the low
spatial resolution, using the parameter SNRqw, d , depending on
the transmitted beamwidth in the measurement of dynamic
motion. The measurement error increased as the transmitted
beamwidth broadening. The error factor of the lower spatial
resolution affected the increase of the measurement error thanthat of the lower transmitted power. The measurement errorof the focused wave was very low since the same frame rate
was used as the diverging waves in the present experiment.
However, the measurement error caused by the lower
temporal resolution will increase when using focused waves
because the measurements using the focused beams become alower frame rate than those using the diverging beams. In the
future study, we will determine the optimal transmitted
conditions for dynamic measurements by additionally examining the error factor of temporal resolution which was notconsidered in the present study. The acceptable range of themeasurement error for the dynamic measurement, which may
depend on the dynamic property of the target tissue, will bealso examined in future work.
Acknowledgments
19K22943.

This work was supported in part by JSPS KAKENHI

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