Japanese Journal of Applied
Physics

You may also like

REGULAR PAPER

Transmission conditions for clear depiction ofthoracic spine based on difference between
reflection and scattering characteristics of medical
ultrasoundTo cite this article: Taiga Bando et al 2022 Jpn. J. Appl. Phys. 61 SG1068- Challenges in Scientific Data
Communication from Low-mass Interstellar
ProbesDavid G. Messerschmitt, Philip Lubin and
Ian Morrison- A simple Peltier cold trap aperture forprotection of vacuum UV optics against
hydrocarbons and reliable calibration of
VUV spectrometers using D2 lamps
Marcel Fiebrandt and Peter Awakowicz- Study on radar scattering characteristics ofdouble S-shaped nozzles with different
aspect ratio
Xiang Gao, Yongqiang Shi and Yiwen Li

View the article online for updates and enhancements.

This content was downloaded from IP address 130.34.32.223 on 03/06/2022 at 03:39

REGULAR PAPER

Japanese Journal of Applied Physics 61, SG1068 (2022)
https://doi.org/10.35848/1347-4065/ac51c0

Transmission conditions for clear depiction of thoracic spine based on difference
between reflection and scattering characteristics of medical ultrasoundTaiga Bando1, Shohei Mori2, Mototaka Arakawa1,2*, Eiko Onishi3, Masanori Yamauchi3, and Hiroshi Kanai1,2
1Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan3
Department of Anesthesiology and Perioperative Medicine, Tohoku University School of Medicine, Sendai 980-8575, Japan2*

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

Received November 2, 2021; revised January 13, 2022; accepted February 2, 2022; published online May 31, 2022
In epidural anesthesia, it is difficult to specify the puncture position of the anesthesia needle. We have proposed an ultrasonic method to depict thethoracic spine using the different characteristics of reflection from bone and scattering from muscle tissue. In the present paper, we investigated thetransmission aperture’s width of the ultrasound probe to emphasize the differences in the reflection and scattering characteristics. First, we
determined the optimum transmission aperture’s width using a simulation experiment. Next, we measured reflection and scattering signals bychanging the transmission aperture’s width in a water tank experiment and confirmed that the results corresponded to the simulations. However, as
the transmission aperture’s width increased, the lateral resolution at the focal point improved. Therefore, better imaging of the human thoracic
vertebrae can be achieved by selecting the transmission aperture’s width, which considers the effect on lateral resolution.
© 2022 The Japan Society of Applied Physics

1. Introduction

Epidural anesthesia is a local anesthesia method used before
surgery, and it is often combined with general anesthesia
because it reduces the burden on patients intraoperatively andpostoperatively.1) The anesthesia needle is punctured fromthe surface of the skin into the spinal space. In epidural
anesthesia for the thoracic spine, it is not easy to puncture theanesthesia needle into the proper position because the spinal
space is narrow and complex. As the location of the punctureis determined by the physician’s palpation at present, thesuccess of anesthesia is dependent on the skills of thephysician. The success rate of epidural anesthesia ranges
from 75% to 94%,2–4) and its failure may induce headaches
and complications. During epidural anesthesia, patients
reported back pain and psychological distress in 22% and
14% of the cases, respectively.5)
Medical ultrasound conﬁrms the puncture position before
anesthesia as an aid of palpation in clinical practice.6) In
epidural anesthesia for the lumbar spine and other regional
anesthesia, ultrasound guidance is often used, and its usefulness
has been demonstrated.7–10) However, it is difﬁcult to depict
clear images of the puncture position, especially for obese
patients with a deep spine or thoracic vertebrae with a narrowgap.11–13) Several studies have been proposed for the ultrasoundguidance of epidural anesthesia, e.g. automatic identiﬁcation of
the spine.14–16) However, these studies targeted the lumbar
spine, which has a wide gap and simple structure.
Ultrasound imaging of bone is studied in the ﬁeld of
orthopedics.17–20) Several methods have been proposed, e.g.
using strain under pressure to identify the bone shape,21,22)
phase symmetry,23) and shadow peaks.24) However, it is
difﬁcult to apply these methods to the thoracic spine because
it is located deep beneath the skin surface and has a complex
surface structure.
We have developed an imaging method that can beapplied to assist epidural anesthesia in the thoracic spine.
In our previous study, we proposed three methods. The ﬁrst
method improves the delayed addition misalignment causedby the reﬂection of ultrasound at the thoracic vertebral
surface,25) and it depicts a smooth and tilted object by notconsidering the transmitting and receiving positions as thesame, applying the envelope method26) and range point
migration method.27,28) The second method is based on the
difference in ultrasound characteristics between soft tissue
and bone,29) which calculates the ratio of the delayed
addition with a wide range along the time direction to thenormal one and multiplies it by the brightness value at eachpoint of the image. The third method is based on the
difference between the reﬂection and scattering ultrasoundcharacteristics.30) This method uses angular amplitude characteristics, which are enveloped amplitudes of signals
received by many elements of the ultrasonic probe at thetime corresponding to the depth of the target. This method
estimates whether the target is a reﬂector or scatterer byﬁtting angular amplitude characteristics obtained from thetarget with the reference data of reﬂection and scatteringcharacteristics. The difference in the angular amplitude
characteristics between reﬂection and scattering affects theestimation accuracy of the target.
The purpose of the present paper is to investigate theultrasound transmission condition so that the difference inangular amplitude characteristics between reﬂection andscattering is more emphasized in the third method. We
fundamentally investigated the difference among angular
amplitude characteristics and the difference in the width of
the transmission aperture.31) Focusing on the transmission
aperture, the effect of the aperture on the angular amplitude
characteristics of scattering and reﬂection was examined bysimulation. Based on the results, a better transmission
aperture is determined by the simulation. Finally, simulation
results were conﬁrmed using water tank experiments.
2. Principle
2.1. Difference of angular amplitude characteristics
between scattering and reflection

Figure 1 shows a wave scattered from a point scatterer whena focused wave is transmitted with a linear probe, where dand xm are the depth of the point scatterer and the lateralposition of the m th received element, respectively, xm = 0
shows the center of the probe aperture, and c is the speed ofsound in the medium. The time ranging from transmission at

SG1068-1© 2022 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 61, SG1068 (2022)

T. Bando et al.
(a)

(b)

Fig. 1. Transmission and reception of a focused wave by a linear array probe.

Fig. 2. (Color online) Simulation of the received signal. (a) Calculation ofyksi m (t ). (b) Received waveform transmitted by one element, y0 (t ).

å RR (m ; d ) RS (m ; d )Aˆ = m,å m {RS (m ; d )}2

the center element to the receipt of the wave scattered fromthe point scatterer at the m th received element, tm, d , isgiven bytm, d =d+d 2 + xm2.
(1 )c
By deﬁning the ideal delay time by {tm, d } and the received
signal at m th element by ym (t ), the angular amplitude
characteristic R (m; d ), which shows the head amplitude of
the ym (t ) just at the ideal delay time tm, d , is provided by theenveloped amplitude y¢ m (t ) of ym (tm, d ) asR (m ; d ) = y¢ m (tm, d ).

(2 )When an ultrasound is irradiated to a scatterer such asmuscle tissue, the ultrasound is scattered along with all the
directions from the object, which follows Rayleigh scattering
when the scatterer is sufﬁciently smaller than the wavelengthof the ultrasound and the angular amplitude characteristic
RS (m; d ) for the scattering becomes a gentle parabola.30) On
the other hand, when ultrasound is irradiated to a reﬂector
with a regional plate, such as a bone, the ultrasound is
specularly reﬂected, and RR (m; d ) for the reﬂection becomeshigh for the direction corresponding to the specular reﬂection
and low for other directions.30)
2.2. Evaluation method for differences in angular
amplitude characteristics
The difference between RR (m; d ) and RS (m; d ) was quantitatively evaluated using following the root mean square error(RMSE):
ˆ S (m ; d )}2
å m {RR (m ; d ) - AR
RMSE [%] =´ 100,
å m RR (m ; d )2

(4 )where Â is the parameter that minimizes the RMSE. From
ˆ In the present paper, a¶RMSE /¶A = 0, we can determine A.
suitable transmission aperture was determined so that the
RMSE becomes maximum for various transmission aperture
widths.
2.3. Simulation method
Figure 2(a) shows the simulation done in this paper. The
number of received elements was 96, and the element pitch
was 0.2 mm, assuming the typical ultrasound diagnostic
equipment with the linear probe. When the short axis of amolybdenum wire with a diameter of 30 μm was set in awater tank, the transmitted and received waveform using one
element above the wire was measured using ultrasounddiagnostic equipment at a center frequency of 7.5 MHz. The
waveform sampled at 40 MHz was interpolated 50 times
using the sinc function, and the resultant y0 (t ) is shown in
Fig. 2(b).
The received signals from a reﬂector or scatterer weregenerated when a focused wave with a focal depth of 30 mm
was transmitted. In Fig. 2(a), yksi m (t ), which is transmitted
from the k th transmitted element, scattered by i th point
scatterer si , and received by m th received element, is given byyksi m (t ) = S (k , x si , z si , m) y0 (t - tksi m) ,(5 )where S (k , x si , z si, m ) shows theoretical scattering characteristics,(3 )SG1068-2

S (k , x si , z si , m)
= A (k , x si , z si , m) s (k , x si , z si , m)
D (x si , z si , m) E (x si , z si , m) ,(6 )© 2022 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 61, SG1068 (2022)

T. Bando et al.

(a)

(b)

Fig. 3. (Color online) Water tank experimental system. (a) The measurement of the scattering characteristics. The short axis of a molybdenum wire with adiameter of 30 mm was measured as a scatterer. (b) The measurement of the reﬂection characteristics. The surface of an acrylic block was measured as areﬂector.

(a1)

(a2)

(b1)

(b2)

Fig. 4. (Color online) Simulation results of the scatterer. (a1), (b1) Received signals ykm (t ) from each transmitted element. (a2), (b2) Received signals ym (t );(a1), (a2) results for x = 0 mm; and (b1), (b2) results for x = -4.8 mm.

A (k , x si , z si , m) = 10-a (lksi+ lsi m ) f0 / 20 ,2

and tksi m shows the delay time of propagation from the k thtransmitted element, i th point scatterer si , and m th received
element aslks
ls mtksi m = i + i + tk ,cw
cw

s (k , x si , z si , m) µ

(7 )where cw is the speed of sound in the medium, lksi and l si m are
the path lengths from the kth transmitting element to si and fromsi to mth receiving element, respectively, and tk is the delay timeof the kth element to transmit the focused wave. S (k , x si , z si, m )of Eq. (6) comprises the propagation attenuation
A (k , x si , z si, m ), the angular characteristic of Rayleigh scattering s (k , x si , z si, m ), the reception directivity of piezoelectricelements D (x si , z si, m ), and the effect of interference in thewidth of the piezoelectric element at the reception of ultrasound,E (x si , z si, m )32), A (k , x si , z si, m ), s (k , x si , z si, m ), andD (x si , z si, m ) are shown in Eqs. (8)–(10), respectively.

1 + cos2 qksi m,
2

D (x si , z si , m) = cos2 qmML,

(8 )
(9 )
(10)

where a is the attenuation coefﬁcient of water(a = 1.94 ´ 10-4 dB MHz-2 mm-1)33); f0 = 7.5 MHz,
which is the center frequency of the probe used in the watertank experiments; qksi m is the scattering angle and is deﬁned
asx s - xk
xm - x si,
qksi m = tan-1 i+ tan-1
(11)
z si
z si
and qmML is the incidence angle from the acoustic matchinglayer to the piezoelectric element given by

SG1068-3© 2022 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 61, SG1068 (2022)

T. Bando et al.

xm - x si ⎞cqmML = sin-1 ⎛⎜ ML ·⎟,clsi m ⎠
⎝ w

(12)

where cML is the speed of sound in the acoustic matchinglayer. By considering scattering, ykm (t ) transmitted from the kth element and received by the m th element is given byykm (t ) = å yksi m (t ).

(13)

si

By adding {ykm (t )} to the transmitted elements {k}, thereceived signal at the m th received element ym (t ) is obtained
as follows:ym (t ) = å ykm (t ).
(14)k

In the actual measurement, ym (t ) is observed at the m thelement and each component of {ykm (t )} cannot be detected.
However, by the simulation experiments in the present paper,ym (t ) is decomposed into the element signals {ykm (t )} of
Eq. (13).
Alternatively in the present paper, we investigated
R (m; d ) of Eq. (2) by clarifying the difference of {ykm (t )}between the reﬂector and scatterer through the simulation
experiments for each of the transmission aperture’s widthsℓw (the number Nw of transmitting elements) of 19.2
(96 elements), 14.4 (72 elements), 9.6 (48 elements), 4.8(24 elements), and 0.2 mm (1 element). The signal from aplate reﬂector was generated by adding all the signals
received from point scatterers aligned densely at 20 μm
intervals with a width of 50 mm. By aligning point scatterers
at 20 μm intervals on a tilted line, the surface of the tilted
reﬂector was simulated.
2.4. Water tank experiments
The ultrasound diagnostic equipment was ProSound SSDα10 (Hitachi Aloka) with a sampling frequency of 40 MHz.
A linear probe UST-5412 (center frequency: 7.5 MHz,
number of elements: 192, and element pitch: 0.2 mm) was
attached to the ultrasound diagnostic equipment. For transmission, each element was given a delay time so that the
focal point was 30 mm, which simulated the depth from theskin surface to the thoracic spine. No apodization was applied
for transmission and reception.
Figure 3 shows the water tank experimental system.
The short axis of molybdenum wire with a diameter of
30 μm and the surface of an acrylic block were used as ascatterer and a reﬂector, respectively. The depths of bothobjects were 30 mm. The angular amplitude characteristics{R (m; d )} acquired with changing the transmission aperture’s widths {ℓw} were compared with the simulation
results.
3. Results and discussion
3.1. Angular amplitude characteristics of scattering

Fig. 5. (Color online) Simulation results of the reﬂector. The dashed lines
represent the ideal delay time tm, d . (a1)–(c1) received signal ykm (t ) from eachtransmitted element; (a2)–(c2) received signals ym (t ); (a1)–(a3) results for
x = 0 mm; (b1)–(b3) results for x = -2.8 mm; (c1)–(c3) results for
x = -4.8 mm.

First, we discuss the simulation results of angular amplitude
characteristics {RS (m; d )} of scattering for a transmission
aperture’s width (ℓw ) of 19.2 mm (96 transmitted elements).
The received element number of m = 47 at the center
position was set to x = 0 mm. Figures 4(a1) and 4(b1)show the received signals ykm (t )∣m = 47 and ykm (t )∣m = 23 at thereceived positions x = 0 and -4.8 mm, respectively, foreach k th transmitted element. The dashed lines in these

SG1068-4© 2022 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 61, SG1068 (2022)

T. Bando et al.

(a1)

(a2)

(b1)

(b2)

(c1)

(c2)

(d1)

(d2)

(e1)

(e2)

Fig. 6. Simulated angular amplitude characteristics of reﬂection and scattering for the different transmission aperture. (a1)–(e1) Reﬂection characteristics;(a2)–(e2) scattering characteristics; (a1), (a2) results for ℓw = 19.2 mm; (b1), (b2) results for ℓw = 14.4 mm; (c1), (c2) results for ℓw = 9.6 mm; (d1), (d2)results for ℓw = 4.8 mm; (e1), (e2) results for ℓw = 0.2 mm.

SG1068-5© 2022 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 61, SG1068 (2022)

T. Bando et al.

Fig. 7. (Color online) RMSE of the angular amplitude characteristics
between reﬂection and scattering at different transmission aperture’s widths{ℓw}. Red dots show the results of the simulation experiment. Blue dots show
the results of the water tank experiment.

Fig. 8. (Color online) Simulation results of the reﬂector with a transmission aperture of 4.8 mm. The dashed lines represent the ideal delay time tm, d .
(a1), (b1) Received signal ykm (t ) from each transmitted element; (a2), (b2)received signals ym (t ); (a1)–(a2) results for x = 0 mm; (b1), (b2) results for
x = -4.8 mm.

ﬁgures show the ideal delay time {tm, d } calculated using
Eq. (1). By integrating {ykm (t )∣m = 47 } and {ykm (t )∣m = 23 } along
the direction of the transmitted elements {k}, Figs. 4(a2) and4(b2) show the resultant waveforms of ym (t )∣m = 47 andym (t )∣m = 23 .
As shown in Figs. 4(a1) and 4(b1), {ykm (t )} were received
at the same time for each received element when the object
was a scatterer and placed at the focal point. Thus, the shapeof ym (t ) was the same as that of the transmitted and received
waveform y0 (t ) based on one element. When the received
position m moved away from above the point scatterer, thesignal amplitude in Fig. 4(b2) decreased owing to thereceiving directivity of elements compared with that inFig. 4(a2).
3.2. Angular amplitude characteristics of reflection
Next, we discuss the simulation results of angular amplitude
characteristics {RR (m; d )} of reﬂection. Figures 5(a1), 5(b1), and5(c1) show the received signals {ykm (t )∣m = 47 }, {ykm (t )∣m = 33 },and {ykm (t )∣m = 23 } at x = 0, -2.8, and -4.8 mm, respectively.
Figures 5(a2), 5(b2), and 5(c2) show ym (t )∣m = 47 , ym (t )∣m = 33 , andym (t )∣m = 23 at x = 0, -2.8, and -4.8 mm, respectively.
Figures 5(a3), 5(b3), and 5(c3) show the amplitudes of thereceived signals ykm (tm, d )∣m = 47 , ykm (tm, d )∣m = 33 , andykm (tm, d )∣m = 23 at the ideal delay time tm, d .
In Figs. 5(a1), 5(b1), and 5(c1), {ykm (t )} was received
earlier than the ideal delay time tm, d when the target was thereﬂector. This is because the propagation paths are shorter
than those when the ultrasound is scattered at the focal point.
Therefore, as shown in Figs. 5(a3), 5(b3), and 5(c3),{ykm (tm, d )} are not constant for the transmitted elements k.
The following two things can be found in Fig. 5(a3). The
ﬁrst is that the angular amplitude characteristic
RR (m = 47; d ) at the central received element m = 47 has
positively large amplitudes for 24 transmitted elements withk = 36–59. The second is that RR (m = 47; d ) is negative forthe transmitted elements around k = 30 and 65. By comparing Figs. 5(a3), 5(b3), and 5(c3), the proﬁle of {ykm (tm, d )}moved toward the transmitted elements on the right side. As aresult of this movement, the negative components aroundk = 65 in Fig. 5(a3) were not received at m = 23, as shownin Fig. 5(c3).
3.3. Relationship between the width of the transmission aperture and angular amplitude characteristics
Figure 6 shows angular amplitude characteristics of reﬂection
and scattering when the transmission aperture’s width ℓw (thenumber Nw of transmitting elements) was 19.2 (Nw = 96),14.4 (Nw = 72), 9.6 (Nw = 48), 4.8 (Nw = 24), and 0.2 mm(Nw = 1). The shape of RR (m ) signiﬁcantly changed as ℓw
decreased, but the maximum value did not signiﬁcantly
change, except when ℓw = 0.2 mm. On the other hand, theshape of RS (m ) did not change, although its amplitudedecreased in proportion to the decrease in ℓw.
This difference is caused by the fact that {ykm (tm, d )} for the
scattering were almost the same among the transmitted
elements [Figs. 4(a1) and 4(b1)], whereas {ykm (tm, d )} forthe reﬂection signiﬁcantly varied among the transmitted
elements [Figs. 5(a3), 5(b3), and 5(c3)]. The decrease in ℓw
corresponds to the exclusion of signals at both ends shown in
Figs. 5(a3), 5(b3), and 5(c3).
For reﬂection, as the received element position (m )departed from the center, the shape of {ykm (tm, d )} changed

SG1068-6© 2022 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 61, SG1068 (2022)

T. Bando et al.

(a1)

(a2)

(b1)

(b2)

(c1)

(c2)

(d1)

(d2)

Fig. 9. Simulation results of angular amplitude characteristics of reﬂection for different transmission aperture’s widths {ℓw}. (a1)–(d1) Results for a reﬂector
tilted by 5° with respect to the probe surface; (a2)–(d2) results for a reﬂector tilted by 10° with respect to the probe surface; (a1), (a2) results for ℓw = 19.2 mm;(b1), (b2) results for ℓw = 14.4 mm; (c1), (c2) results for ℓw = 9.6 mm; (d1), (d2) results for ℓw = 4.8 mm.

[Figs. 5(a3), 5(b3), and 5(c3)], and the transmitted elements{k} with large amplitudes of {ykm (tm, d )} shifted toward theend. Therefore, as ℓw decreased, RR (m ) became small.
The RMSE between {RR (m; d )} and {RS (m; d )} for eachtransmission aperture’s width (ℓw ) is denoted with red dots in
Fig. 7. The cases of ℓw = 2.4 mm (Nw = 12) and ℓw = 7.2 mm(Nw = 36) were also calculated and added. The case of ℓw= 4.8 mm (Nw = 24) can emphasize the difference.
Figures 8(a1) and 8(b1) show the received signals{ykm (t )∣m = 47 } and {ykm (t )∣m = 23 } at x = 0 and 4.8 mm foreach k th transmitted element, respectively, for ℓw = 4.8 mm(Nw = 24). Figures 8(a2) and 8(b2) show the received signal
ym (t ) at x = 0 and -4.8 mm, respectively. Figures 8(a3) and8(b3) show the amplitudes of the received signals{ykm (tm, d )∣m = 47 } and {ykm (tm, d )∣m = 23 } at the ideal delay times
tm, d , respectively.
The reason for the RMSE being maximized for ℓw= 4.8 mm (Nw = 24) can be explained in two points: ﬁrst,
as shown in Fig. 8(a3), when ℓw was 4.8 mm (24 elements) or
more, RR (47; d ) was almost the same for k = 36–59, which
accounted for a large fraction of RR (47; d ) at the center withregard to the received element; second, as shown in

SG1068-7© 2022 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 61, SG1068 (2022)

T. Bando et al.

Fig. 10. (Color online) Simulation results of the RMSE of angular
amplitude characteristics between reﬂection and scattering at different
transmission aperture widths {ℓw}. Red and blue dots show the results for areﬂector tilted by 5° and 10°, respectively.

Figs. 5(a3), 5(b3), and 5(c3), the shape of {ykm (tm, d )}changed as the received element position shifted. Whenℓw = 4.8 mm (Nw = 24), as shown in Fig. 8(b3), for thereceived element position (m ) apart from the center, thereceived signal decreased with the change in {ykm (tm, d )}.
When ℓw is larger than 4.8 mm, the number of transmitted
elements with a large amplitude of {ykm (tm, d )} does notdecrease even if the shape of ykm (tm, d ) changes slightly;
therefore, the width of the peak of RR (m; d ) increases, andthe RMSE with the angular amplitude characteristic of
scattering RS (m; d ) decreases. When ℓw is narrower than
4.8 mm, the peak of RR (m; d ) decreases because all thesignals from the transmitted elements of k = 36–59 have notbeen received. Therefore, the RMSE between RR (m; d ) andRS (m; d ) is maximum when ℓw = 4.8 mm (Nw = 24).
Next, we investigated the case in which the reﬂector was
inclined to the probe surface. Figure 9 shows the angular
amplitude characteristics of reﬂection and scattering when thereﬂector was tilted by 5° or 10° concerning the probe surface.
The signals with large amplitude were detected with the endof the received elements {m} as the tilt angle increased. Whenthe reﬂector was tilted by 10°, the amplitudes decreased withdecreasing ℓw, because most of the reﬂected signals could not
be received at the receiving elements; this was because of thetilt of the reﬂector.
The RMSEs between {RR (m; d )} and {RS (m; d )} for eachtransmission aperture’s width (ℓw ) when the reﬂector wastilted by 5° or 10° to the probe surface are denoted with red
and blue dots, respectively in Fig. 10. When the reﬂector
inclination was 5°, the RMSE was maximum forℓw = 4.8 mm (Nw = 24). The tendency was the same as theresult for the parallel reﬂector in Fig. 7. When the reﬂector
was tilted by 10°, the RMSE also increased with decreasingℓw, although the RMSE for ℓw = 4.8 mm was almost the sameas that for ℓw = 19.2 mm (Nw = 96). This is because most of

the reﬂected signals could not be received at the receiving
elements for ℓw = 4.8 mm. Therefore, it suggests that thebone surface should be aligned as parallel as possible to theprobe surface in clinical applications.
In the simulation, the reﬂector was assumed to be ﬂat;therefore, if the reﬂector was tilted to the probe surface in theelevational direction of the probe, the shape of {RR (m; d )}did not change. However, the angular amplitude characteristics from the curved surfaces such as the thoracic vertebrae
would change due to phase aberration. We will investigate
this effect further in our future work.
3.4. Results of the water tank experiment
Figure 11 shows {RR (m; d )} of reﬂection and {RS (m; d )} of
scattering for each transmission aperture’s width (ℓw ); thesewere obtained from the surface of the acrylic block and theshort axis of the wire, respectively, in the water tankexperiment. The received signal was too weak while measuring the scatterer when ℓw = 0.2 mm. The results were
almost similar to Fig. 6. In Fig. 7, the blue dots show the
RMSE between {RR (m; d )} and {RS (m; d )} for each value ofℓw. Reﬂectors and scatterers can be distinguished in detailwhen ℓw = 4.8 mm.
3.5. Effect of the decreased transmission aperture’s
width on the lateral resolution
The reduction in ℓw affects the lateral resolution of the
focused wave. Figure 12(a) shows the acoustic ﬁeld distribution along the lateral direction x at a focal depth of 30 mm foreach ℓw. The horizontal axis represents the lateral position
centered just above the beam. The vertical axis was normalized to the maximum amplitude for each value of ℓw. The fullwidth-at-half-maximum (FWHM) increased as ℓw decreased.
Figure 12(b) shows the relationship between the FWHM of
the transmitted beam at the focal depth and RMSE of{RR (m; d )} and {RS (m; d )}. There is a trade-off between
the lateral resolution and RMSE. In thoracic spine measurements in the clinic, it is necessary to determine the appropriate transmission aperture’s width ℓw for imaging byconsidering this trade-off relationship.
4. Conclusions

We investigated the ultrasound transmission conditions so thatdifferences in the angular amplitude characteristics of reﬂection and scattering are emphasized more. We discussed theangular amplitude characteristics {RR (m; d )} and {RS (m; d )}of the reﬂection and scattering based on the simulation and thewater tank experiment and clariﬁed the relationship between
the angular amplitude characteristics and transmission aperture’s width ℓw. For the measurement of the human thoracic
vertebrae, it is necessary to consider the effect of the lateral
resolution by changing ℓw and to investigate a suitable ℓw. The
simulation and water tank experimental results showed thatthe difference between {RR (m; d )} and {RS (m; d )} is emphasized more, and it will signiﬁcantly support thoracic epidural
anesthesia in the future.

SG1068-8© 2022 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 61, SG1068 (2022)

T. Bando et al.

(a1)

(a2)

(b1)

(b2)

(c1)

(c2)

(d1)

(d2)

(e1)

Fig. 11. Angular amplitude characteristics of reﬂection and scattering for the different transmission aperture {ℓw} obtained from the water tank experiment.
(a1)–(e1) Reﬂection characteristics, (a2)–(e2) scattering characteristics, (a1), (a2) results for ℓw = 19.2 mm; (b1), (b2) results for ℓw = 14.4 mm; (c1), (c2)results for ℓw = 9.6 mm; (d1), (d2) results for ℓw = 4.8 mm, (e1) results for ℓw = 0.2 mm. At ℓw = 0.2 mm, signals of the scatterer were weak and could not be
detected.

SG1068-9© 2022 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 61, SG1068 (2022)

T. Bando et al.

(a)

(b)

Fig. 12. (Color online) Relationship between the transmission aperture’s
width {ℓw} and the acoustic ﬁeld distribution. (a) Acoustic ﬁeld distribution
along the lateral direction at a focal depth of 30 mm for each transmission
aperture {ℓw}. (b) Relationship between the FWHM of the transmitted beamand the RMSE of the angular amplitude characteristics of reﬂection andscattering at the focal depth.

Acknowledgments

This work was partially supported by JSPS KAKENHI
20H02156.

1) R. D. Miller, L. I. Eriksson, J. P. Wiener-Kronish, N. H. Cohen, and W.
L. Young, Miller’s Anesthesia (Saunders, Amsterdam, 2015).
2) C. Konrad, G. Schupfer, M. Wietlisbach, and H. Gerber, Anesth. Analg. 86,
635 (1998).
3) G. Le Coq, B. Le Ducot, and D. Benhamou, Can. J. Anaesth. 45,719 (1998).
4) M. P. Lewis, P. Thomas, L. F. Wilson, and R. C. Mulholland, Anesthesia 47,
47 (1992).
5) B. Finucane, Complications of Regional Anesthesia (Springer, New York,
2009).
6) M. Yamauchi, Trends Anaesth. Crit. Care 2, 234 (2012).
7) M. Nassar and I. A. Abdelazim, J. Clin. Monit. Comput. 29, 573 (2015).
8) C. Alwin, Anesthesia 33, 674 (2020).

9) B. Grosse, S. Eberbach, H. O. Pinnschmidt, D. Vincent, M. SchmidtNiemann, and K. Reinshagen, BMC Anesthesiol. 20, 256 (2020).
10) J. A. Lim, S. Y. Sung, J. H. Lee, S. Y. Lee, S. G. Kwak, T. Ryu, and W.
S. Roh, Medicine 99, e21684 (2020).
11) T. Grau, R. W. Leipold, S. Delorme, E. Martin, and J. Motsch, Reg. Anesth.
Pain Med. 27, 200 (2002).
12) M. Tiouririne, A. J. Dixon, F. W. Mauldin Jr, D. Scalzo, and A. Krishnarai,
Invest. Radiol. 52, 447 (2017).
13) H. Raﬁ-Tari, V. A. Lessowav, A. A. Kamani, P. Abolmaesumi, and
R. Rohling, Ultrasound Med. Biol. 41, 2220 (2015).
14) M. Pesteie, V. Lessowav, P. Abolmaesumi, and R. N. Rohling, IEEE Trans.
Med. Imaging 37, 81 (2018).
15) T. T. Oh, M. Ikhsan, K. K. Tan, S. Rehena, N. R. Han, A. T. H. Sia, and B.
L. Sng, BMC Anesthesiol. 19, 57 (2019).
16) N. Quader, A. Hodgson, and R. Abugharbieh, CLIP@MICCAI, 2014, p. 76.
17) F. Ozdemir, E. Ozkan, and O. Goksel, Conf. Proc. Medl Image Comput
Asiist Interv., 2016, p. 256.
18) S. Yu, K. K. Tan, B. L. Sng, S. Li, and A. T. H. Sia, Proc. IEEE 12th Int.
Symp. Biomed Imag, 2015, p. 243, 10.1109/ISBI.2015.7163859.
19) T. T. Y. Lee, W. W. Jiang, C. L. K. Cheng, K. K. L. Lai, M. K. T. To, R.
M. Castelein, J. P. Y. Cheung, and Y. P. Zheng, Ultrasound Med. Biol. 45,2725 (2019).
20) Y. S. Wong, K. K. L. Lai, Y. P. Zheng, L. L. N. Wong, B. K. W. Ng, A. L.
H. Hung, B. H. K. Yip, W. C. W. Chu, A. W. H. Ng, and Y. Qiu, UltrasoundMed. Biol. 45, 2866 (2019).
21) S. F. Eby, P. Song, S. Chen, Q. Chen, J. F. Greenleaf, and K. N. An, J.
Biomech. 46, 2381 (2013).
22) M. A. Hussain, A. J. Hodgson, and R. Abugharbieh, Ultrasound Med. Biol.
43, 648 (2017).
23) I. Hacihaliloglu, R. Abugharbieh, A. J. Hodgson, and R. N. Rohling,
Ultrasound Med. Biol. 35, 1475 (2009).
24) P. Pandey, N. Quader, K. Mulpuri, P. Guy, R. Garbi, and A. J. Hodgson,
Epic Series Health Sci. 3, 301 (2019).
25) K. Takahashi, H. Taki, E. Onishi, M. Yamauchi, and H. Kanai, J. Appl.
Phys. 56, 07JF01 (2017).
26) T. Sakamoto, H. Taki, and T. Sato, Acoust. Sci. Technol. 32, 143 (2011).
27) S. Kidera, T. Sakamoto, and T. Sato, IEEE Trans. Geosci. Remote Sens. 48,
1993 (2010).
28) H. Taki, S. Tanimura, T. Sakamoto, T. Shiina, and T. Sato, J. Med.
Ultrasonics 48, 51 (2015).
29) T. Yokoyama, S. Mori, M. Arakawa, E. Onishi, M. Yamauchi, and
H. Kanai, J. Med. Ultrasonics 42, 3 (2019).
30) T. Hashimoto, S. Mori, M. Arakawa, E. Onishi, M. Yamauchi, and
H. Kanai, J. Appl. Phys. 60, SDDE15 (2021).
31) T. Bando, S. Mori, M. Arakawa, E. Onishi, M. Yamauchi, and H. Kanai,
Proc. Symp. Ultrason. Electr., 2021, Vol. 41.
32) T. Hashimoto, S. Mori, M. Arakawa, E. Onishi, M. Yamauchi, and
H. Kanai, Proc. Autumn Mtg. Acoust. Soc. Jpn., 2020, p. 76.
33) Y. Hashimoto, N. Akashi, and J. Kushibiki, “Measurements of ultrasonicattenuation coefﬁcients of water in VHF/UHF range,” IEICE Tech. Rep.
US97-50, 1997, [in Japanese].

SG1068-10© 2022 The Japan Society of Applied Physics