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A study on differentiation of depiction between scatterer and reflector toassist epidural anesthesia by ultrasoundTo cite this article: Takumi Hashimoto et al 2021 Jpn. J. Appl. Phys. 60 SDDE15

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REGULAR PAPER

Japanese Journal of Applied Physics 60, SDDE15 (2021)
https://doi.org/10.35848/1347-4065/abf4a3

A study on differentiation of depiction between scatterer and reflector to assist
epidural anesthesia by ultrasoundTakumi Hashimoto1, 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 December 4, 2020; revised March 10, 2021; accepted April 2, 2021; published online April 28, 2021
A sharp depiction of the puncture point of the needle by differentiating muscle and bone is required for ultrasound-guided epidural anesthesia in thethoracic spine. In the present paper, we proposed a method for depicting the thoracic vertebral surface by utilizing the difference between
scattering and reflection characteristics. This method estimates whether an object is a scatterer or a reflector referring to the scattering andreflection characteristics acquired in the water tank experiment. The proposed method was applied to basic experiments and in vivo experiments.
In the basic experiments, the matching using root mean squared error allowed us to differentiate the depiction between scattering and reflection. In
the in vivo experiment, we were able to estimate the position of the bone as a reflector and the slope was generally correct.
© 2021 The Japan Society of Applied Physics

1. Introduction

Epidural anesthesia is one of the local anesthesia before
surgery. It is often used in combination with general anesthesia
because it has a great advantage in reducing the burden ofpatients both intraoperatively and postoperatively.1) The anesthesia needle is inserted into the spinal gap through the skinsurface. In epidural anesthesia, especially in the thoracic spine,
it is difﬁcult to inject the needle into the proper position
because of the narrow spinal gap. Currently, the success ofanesthesia strongly depends on the skill of the physician, since
the puncture position is mainly detected by palpation. The
failure rate of epidural anesthesia has been reported to be
6%–25%.2–4) At the time of epidural anesthesia, 22% and 14%
of patients reported back pain and psychological distress,
respectively.5) Moreover, the failure of anesthesia leads toheadaches and complications.
Medical ultrasound is used to identify the puncture
position before anesthesia as an aid of palpation in theclinic.6) Epidural anesthesia for the lumbar spine and otherlocal anesthesia techniques, such as the iliac inguinal gastric
block and the femoral nerve block, are commonly used withultrasound guidance.7–10) However, medical ultrasound does
not provide a clear image of the puncture location for patientswith deep spinal positions, such as obese patients.11–13)
Studies aimed at ultrasound guidance of epidural anesthesia,
such as automatic identiﬁcation of the spine, have been
proposed,14–16) but these studies have been aimed to apply on
the lumbar spine, which has a wide gap and a simple
structure.
Ultrasound imaging of bone has been studied in the ﬁeld of
orthopedics.17–21) For example, some methods have been
proposed to identify the shape of the bone using the strain of
the pressurized bones,22,23) phase symmetry,24) or shadow
peaks.25) However, it is difﬁcult to apply these methods to thethoracic spine because it is located deep from the skin surface
and has a complex surface structure.
We have been studying the imaging methods to accurately
guide epidural anesthesia for the thoracic spine. The aim is tosuppress the depiction of muscle and emphasize that of bone
to sharply depict the position of the needle insertion, and two

methods were previously proposed. The ﬁrst was to improvethe misalignment of the delayed addition that occurs in theultrasound reﬂected from the thoracic spine surface.26) Thismethod depicts a smooth and tilted object by considering thetransmitting and receiving positions not to be the same basedon the envelope method27) and the range point migration
method.28,29) The other method utilized the different ultrasound properties between soft tissues and bone.30) In thismethod, the ratio of an averaged delayed sum in a wide
region around the ideal delay time to an ordinary delayed
sum was calculated and multiplied to the luminance value ofthe B-mode image. As a result, we succeeded in suppressing
the depiction of muscle and soft tissues for the most part, butsome muscle tissues still remained. A problem of the
proposed method in a previous study30) was to calculate theaverage power of the enveloped signals in the depth direction. Therefore, the previous method also enhanced the
depiction of the objects other than the bones such as thescatterers around them and the dense muscle tissues whenreﬂected waves from the objects other than the observation
point were involved within the averaged region. In thepresent study, we investigate the scattering and reﬂection
properties of ultrasound for muscle and bone in more detail.
We have succeeded in estimating the inclination of a planereﬂector by the normalized cross-correlation, utilizing that thereﬂection property of ultrasound shifts to angle direction
according to the inclination of the reﬂector.31) However, thedifferentiation of the depiction of scattering and reﬂection
was not investigated. The purpose of the present paper is toclearly depict the thoracic spine gap, which is the puncture
location, by differentiating between scatterers and reﬂectors
in the depiction. We compare the estimation results of ascatterer and a reﬂector by the normalized cross-correlationand the root means square error (RMSE), and apply the
proposed method in in vivo experiments.
2. Principle and experimental method
2.1. Difference between scattering and reflection ofultrasoundFigure 1 shows schematic diagrams of the scattering andreﬂection of ultrasound waves when a focused wave is

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T. Hashimoto et al.

(a)

(b)

(c)

Fig. 1. (Color online) Differences in angular amplitude characteristics due to scattering and reﬂection of ultrasound. (a) Scattering characteristics, (b)reﬂection characteristics parallel to the probe, and (c) reﬂection characteristics tilted to the probe.

transmitted by a linear probe. Here, θ is the prospective angle
from the surface of the object to the receiver element of theprobe. The angular amplitude characteristics of the received
signals are different for a scatterer, such as muscle tissue, anda reﬂector, such as bone. When a focused ultrasound istransmitted to a scattering object, as shown in Fig. 1(a), theultrasound wave is scattered on the surface of the object in all
directions. The angular dependence of scattering from a point
scatterer is assumed to follow the Rayleigh scattering. The
element also has a directivity when receiving scatteredwaves. However, since the prospective angle θ from thescatterer to the receiving element is small in the present
study, the angular dependence of the amplitude characteristic
R(θ) of the received signal is small in scattering. On the other
hand, when a focused ultrasound is irradiated to an object
with the surface structure parallel to the probe, as shown in
Fig. 1(b), the ultrasound wave is specularly reﬂected on theobject surface. The amplitude of the signal received at eachelement is large in the reﬂection direction and small in theother directions. Therefore, the angular dependence R(θ) islarge in reﬂection.32)
The reﬂection characteristics also depend on the inclination of the reﬂector to the probe. As shown in Fig. 1(c), when
focused ultrasound is transmitted to an object surface tilted
with an angle f to the probe surface, the direction of the main
lobe of the refection beam is shifted by 2f in the θ-axis
direction. As a result, the angular amplitude characteristics ofthe received signal R(θ) change with the structure and theinclination of the target.

2.2. Proposed method

Figure 2 shows the schematic view of the procedure toestimate the slope of an object at a position P (x, z ).31) R(θ)
differs in scattering and reﬂection, and it also depends on
the angle of the reﬂector because the transmitted beam has awidth even at a focal point. First, the amplitudes on the ideal
delay time corresponding to the reception time of thescattered wave, which is obtained when a point scatterer
is assumed to exist at a position P (x, z ), are extracted fromthe measured data of the ultrasonic probe before the delayand-sum processing, and the angular amplitude characteristic R (q; P) is calculated (Step I). By matching theobtained characteristic R (q; P) with the scattering characteristic RS (q; zR ) and the reﬂection characteristics group{RR (q; zR, f )}, which were obtained in a water-tank
experiment in advance, we estimate whether the object isthe scatterer or the reﬂector, and its angle if it was estimatedas the reﬂector (Step II). The reference data was acquired sothat the focal depth of the focused wave was equal to thedepth of the object, zR. Two methods were investigated forthe matching. The ﬁrst one is the normalized cross correlation. The normalized cross correlation with the reference
data of the scattering property and the reference data of thereﬂection properties are shown in Eqs. (1) and (2), respectively.

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rS (P) =1å w (q){R (q; P) - R (q; P)}
NsP sS q´ {RS (q ; zR) - RS (q ; zR)},(1 )© 2021 The Japan Society of Applied Physics

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Fig. 2. (Color online) Flow of estimating the slope of an object.

r R (f ; P) =1
å w (q){R (q; P) - R (q; P)}
NsP sR, f q(2 )RMSES (P) =´ {RR (q ; zR , f) - RR (q ; zR , f)},sS =sR, f =(6 )1
å [w (q){R (q; P) - R (q; P)}2 ] ,
N q

(3 )

1
å [w (q){RS (q; zR) - RS (q; zR )}2 ] ,
N q

(4 )

1
å [w (q){RR (q; zR , f) - RR (q; zR , f)}2 ] ,
N q

(5 )

sP =

å q w (q){R (q; P) - Aˆ S (P) RS (q; zR)}2 ,å q w (q){R (q; P)}2

RMSER (f ; P)=

å q w (q){R (q; P) - Aˆ R (f ; P) RS (q; zR)}2 ,å q w (q){R (q; P)}2åqAˆ S (P) =w (q ) R (q ; P) RS (q ; zR)

å q w (q){RS (q; zR)}2

where R̄ is the mean value of the amplitude angle characteristics, σ is the standard deviation of the amplitude angle
characteristics, and w (q ) is the window function forweighting the correlation. In the present study, we used arectangular window with a value of 1 for all θ. The normalized cross correlation can evaluate the similarity regardless of
the amplitude component by removing the DC component of
the amplitude and normalizing it by the standard deviation.
The object and the angle are estimated from the matching
result in which the measured amplitude characteristic is thehighest correlation with the reference data.
The second matching method is based on calculating the
RMSE. Equations (6) and (7) show the RMSEs withthe reference data of the scattering characteristics and thereference data of the reﬂection characteristics, respectively.

åqAˆ R (f ; P) =,w (q ) R (q ; P) RR (q ; zR , f)

å q w (q){RR (q; zR , f)}2

(7 )

(8 )

,

(9 )

where AˆS (P) and AˆR (f; P) are the parameters to minimize
the RMSE between the two characteristics. Using¶RMSES (P) /¶AS (P) = 0 and ¶RMSER (f ; P) / ¶AR (f ; P) = 0,
we can calculate AˆS (P) and AˆR (f; P). The window functionw (q ) for weighting the RMSE is the same as that for thenormalized cross correlation. The object and the angle are
estimated from the matching result in which the value of
the RMSE between the measured amplitude characteristic andthe reference data is the lowest.
The estimated results are superimposed on each point
P (x, z ) in the B-mode image (Step III). Accordingly, thismethod will locally estimate whether an object is a scatterer
or a reﬂector. The previous method calculated the average ofthe power of the enveloped signal for 9 wavelengths in the

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depth direction.30) In contrast, this method uses only theenveloped amplitudes of the ideal delay time. Therefore, thismethod can greatly reduce the effect of the reﬂected waves
from the objects other than the observation point P( x, z )compared to the previous method.
2.3. Experimental method
The purpose of the present study is to differentiate thedepiction of scattering and reﬂection by using the received
signals from a scatterer and a reﬂector acquired in the watertank experiments as reference data. We estimated the object
using data acquired from the basic experiments and in vivo
experimental results for human thoracic vertebrae. The
ultrasonic diagnostic apparatus was Hitachi Aloka a10 witha sampling frequency of 40 MHz. A linear probe, UST-5412,
with 192 elements was attached to the diagnostic apparatus.
The transmission frequency was 7.5 MHz. 96 elements wereused in a single transmission and reception. The spacing
between elements was 0.2 mm. The focal point for thetransmission was set at 30 mm. No apodization was applied
for transmission and reception.
Figure 3 shows a schematic diagram of the water-tank
experimental system. First, the angular characteristics ofscattering and reﬂection were measured. We measured ashort axis of a tungsten wire as a scatterer and an acrylic
block as a reﬂector. In the present paper, the muscle wasassumed to be a scatterer and simulated by the wire. Bone
was assumed to be a reﬂector and simulated by the surface of
the acrylic block. The depth of these objects was set atzR = 30 mm from the probe surface. The acrylic block wasmeasured against the probe surface inclined from 0° to 15°
with 1° step. This simulates the tilting of the thoracic spine
against the skin surface. We obtained the scattering andreﬂection characteristics of the reference data, RS (q; zR ) and{RR (q; zR, f )}, as follows. First, the received element position and time where the enveloped amplitude was the largest
among all the received elements was calculated. Second, theideal delay time for each element was calculated referred tothe position and time. Finally, the instantaneous value of theenveloped amplitude of each element was calculated at theideal delay time. The number of sampling points wasinterpolated 8 times for the sampling of 40 MHz to calculate
the angular amplitude characteristics with high accuracy.
(a)Next, the thoracic spine of two healthy men in their 20 s
was measured. The measurement section was set at paracentral visible the dura mater during the puncture. The
measurements were applied while the patient was lied
down and curled up as in the case of anesthesia. The depth
and tilt of the thoracic spine for the subjects were 28–35 mm
and 7°–11°, respectively.
3. Results and discussion
3.1. Result of water-tank experiment

Figure 4 shows the measured results of the scattering andreﬂection characteristics. The measurement result for the
scatterer is shown in Figs. 4(a1)–4(c1) and that for thereﬂector when f = 10 is shown in Figs. 4(a2)–4(c2).
Figures 4(a1) and 4(a2) are the B-mode images, Figs. 4(b1)and 4(b2) are the amplitude data acquired at each element
before the delay-and-sum processing on the yellow line in
Figs. 4(a1) and 4(a2), and Figs. 4(c1) and 4(c2) are theamplitude values on the green dashed lines in Figs. 4(b1) and4(b2). The green curvature is the ideal delay time of thescattered waves from a point scatterer. Comparing Figs. 4(c1)and 4(c2), low angle dependency in scattering characteristics
and high angle dependency in reﬂection characteristics wereconﬁrmed. Figure 5 summarizes the measurement results of
the angular amplitude characteristics. The red line is thescattering property and the blue and black lines are thereﬂection properties. As the slope of the reﬂector increases,
the color of the line becomes bluer. We conﬁrmed that thereﬂective properties shifted in the θ-axis direction according
to the inclination of the reﬂector. The above results wereconsistent with those shown in Fig. 1.
We estimated which object was scatterer or reﬂector, and if
it was a reﬂector how inclination it was using the angular
amplitude characteristics in Fig. 5 as reference. The reﬂection
properties from a negative slope reﬂector were calculated
from those for positive slopes by reversing the properties forequal absolute values of the slope f in the θ-axis direction.
Figure 6 shows the results of the object estimation for thedata acquired at the water-tank experiments. The result forthe scatterer is shown in Figs. 6(a1)–6(c1) and that for thereﬂector when f = 10 is shown in Figs. 6(a2)–6(c2). In
these ﬁgures, Figs. 6(a1) and 6(a2) are the B-mode images,(b)Fig. 3. (Color online) Schematic diagram of the water-tank experimental system. (a) Measurement of scattering characteristics. A very thin tungsten wire
along the short axis direction was measured as a scatterer. (b) Measurement of reﬂective characteristics. The acrylic block was measured concerning the probefrom 0° to 15°at the 1° step.

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(a1)

(a2)

(b1)

(b2)

(c1)

(c2)

Fig. 4. (Color online) Results of the water-tank experiments. (a1)–(c1) Results for a scatterer, (a2)–(c2) results for a reﬂector, (a1), (a2) B-mode image, (b1),(b2) each element data, which is necessary for the image formation on the yellow dashed line of the B-mode image, and (c1), (c2) angular amplitude
characteristics. We plotted the amplitude of the element data on the green line in (b1) and (b2), respectively.

Fig. 5. (Color online) The angular amplitude characteristics measured in
the water-tank experiments. The red line is the scattering property and theblue and black lines are the reﬂection properties.

6(b1) and 6(b2) are the matching results using the normalized
cross correlation, and 6(c1) and 6(c2) are those using the
RMSE. The estimated results were plotted with purple for the
scatterer and the other colors for the reﬂector depending on
the estimated slope. Comparing Figs. 6(b1) and 6(c1), almost
all of the estimates were correct using the RMSE, but there
were many misestimates using the normalized cross correlation. In Figs. 6(b2) and 6(c2), estimates by both methods
were generally correct in estimating the reﬂectors.
3.2. Difference between normalized cross-correlation
and RMSE
In this section, we compared the two matching methods. The
estimated results for the scatterer using the normalized crosscorrelation differed from those using the RMSE. Here, we
discuss the difference in the angular amplitude characteristics
at the matching. For this discussion, we investigated theangular amplitude characteristics obtained at the black dot
P0 (x 0 , zR ) shown in the scatterer estimation results in
Figs. 6(b1) and 6(c1). The depth of P0 was equal to thedepth at which the scattering and reﬂection properties of thereference were acquired.
Figure 7(a) shows the amplitude angle characteristics
obtained at the point P0 (x 0 , zR ) and some of the amplitude
angle characteristics of the reference data. The point
P0 (x 0 , zR ) should be estimated as a scatterer, as there was
one scatterer at the depth equal to the focus of the transmitted
beam. Figure 7(b) shows each angular amplitude characteristic normalized by the standard deviation after removing the
DC component to calculate the normalized cross-correlation.
Figure 7(d) shows the raw data of R (q; P0) and reference data
RS (q; zR ) and {RR (q; zR, f )} after multiplying each of themby the coefﬁcient AˆS (P0) or AˆR (P0 , f ) to calculate theminimal RMSE between R (q; P0) and each reference data.
Focusing on the characteristics of measured scattering (greenline) and referred reﬂection in f = 5 (blue line), they arevery different in terms of angle dependence of amplitude in
Fig. 7(a), although they are very similar in Fig. 7(b). In
contrast, in Fig. 7(d), they are signiﬁcantly different, as wellas in Fig. 7(a). Figure 7(c) shows the calculated results of thenormalized cross correlation between the amplitude angularcharacteristics at the point P0 (x 0 , zR ) and each reference data.
The correlation with the reference data of the scattering
property is shown with the dotted red line. Thus, the result by
the normalized cross correlation did not provide the maximum correlation with the true value (scattering characteristics). Some positions in Fig. 6(b1) were also misestimated.
When the normalized cross correlation is calculated, the DC
component of the waveform is removed and the amplitude isnormalized using the standard deviation. These two processes
reduced the difference of angular dependence of the scattering and reﬂection characteristics, and false estimation wascaused because the similarity between the scattering andreﬂection reference data became higher than that before theprocessing.

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(a1)

(a2)

(b1)

(b2)

(c1)

(c2)

Fig. 6. (Color online) Results of object estimation using the data from the water-tank experiment. (a1)–(c1) Results for a scatterer, (a2)–(c2) results for areﬂector, (a1), (a2) B-mode images, (b1), (b2) normalized cross-correlation matching, and (c1), (c2) RMSE matching.

On the other hand, when calculating the RMSE, wemultiply the reference data by a constant value such that
the RMSE is minimized. Figure 7(e) shows the calculated
results of the RMSE with each reference data. Thus, the result
using the RMSE was able to correctly estimate the scatterer
in the position where misestimation occurred when using thenormalized cross correlation since the RMSE retains information on the angular dependence of the amplitude angularcharacteristics as shown in Fig. 7(d).
3.3. Result of in vivo experiment
Figure 8 shows the measurement results of the humanthoracic spine for two subjects A and B, respectively. In
these ﬁgures, Figs. 8(a1) and 8(a2) are the B-mode images,
8(b1) and 8(b2) are the locations inferred to be bone andanalysis area, 8(c1) and 8(c2) are the trivalued images with
low-level brightness values, estimated positions as a scatterer,
and estimated positions as a reﬂector, 8(d1) and 8(d2) are the
RMSE results between the angular amplitude characteristics
obtained at each point and the reference scattering characteristics by Eq. (6), and 8(e1) and 8(e2) are the matching results
using RMSE. In Figs. 8(c1) and 8(c2), black points show thepoints where the brightness value was less than −30 dB ofthe maximum value in each B-mode image and the object
estimation was not done at the points. Magenta points
indicate the points where a scatterer is presumed to belocated. Green points indicate where a reﬂector is presumed
to be located. In Figs. 8(e1) and 8(e2), only the points
estimated as the reﬂector were overlapped to the B-mode
image.
The position and inclination of the bones were almost
correctly estimated in both subjects for the estimation ofbone. The result for subject A in Fig. 8(e1) was generally
successful in differentiating the depiction of muscle tissue
and bone because there were few points where muscle tissues
above bone were estimated as the reﬂectors. However, theresult for subject B in Fig. 8(e2) had many points wheremuscle tissues were estimated as the reﬂector. Moreover, inboth subjects, muscle tissues were largely estimated as thereﬂector in the points on both sides of the images.
3.4. Discussion of in vivo result
Bones were almost estimated to be reﬂectors as well as theassumption. Although the muscle was assumed to be ascatterer, there were points where it was estimated to be areﬂector, and there were differences in the estimated results
between the two subjects. In particular, there were many
points where the muscle was estimated to be a reﬂector in theedge of the transmitted beam. The number of elements
available for transmission and reception was decreased forlateral positions of 0–8 mm and 28–36 mm. The reﬂection
characteristics were changed by the lack of the number of

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(a)

(b)

(d)

(c)

(e)

Fig. 7. (Color online) Amplitude angle characteristic at a position P0(x 0 , zR ) where the results for the two matching methods differed. (a) The raw
characteristics before processing, (b) the characteristics for computing the normalized cross correlation, (c) the values of the normalized cross correlation
between R (q; P0) and each reference data. The red dotted line shows the correlation value between R (q; P0) and RS (q; zR ), (d) the characteristics for computing
the RMSE, and (e) the RMSE value of R (q; P0) for each reference data. The red dotted line shows the RMSE value of R (q; P0) for RS (q; zR ).

elements for transmission. The estimation accuracy may bedeclined because the number of received data was decreased,
especially for the large-θ data, where the difference between
the scattering and the reﬂection is obvious, for matching. As
shown in Figs. 8(d1) and 8(d2), the RMSE values of theangular amplitude characteristics from muscle tissues for thereference scattering characteristics were high on both sides.
To further investigate the results of muscle and bone
estimation, the amplitude angular characteristics obtained forthe muscle tissue and the bone for subject B are shown in
Fig. 9. The green lines in Figs. 9(a) and 9(c) show the angular
amplitude characteristics for the muscle tissue obtained at the
point P1(x1, z1) in Fig. 8(b2) and the bone obtained at the point
P2 (x2 , z2 ), respectively. The angular amplitude characteristicof the muscle tissue was expected to have the smallest error
with the scattering characteristic shown by the red line in

Fig. 9(a), however, the result for the refection characteristicwith f = -5 was the smallest in practice. Comparing to thescattering characteristic from a point scatterer, the angular
amplitude characteristics from the muscle tissue showed
greater attenuation of the amplitude at large ∣ q ∣. We expected
RMSES (P) was large at the bone location and small at themuscle location, but as shown in Figs. 8(d1) and 8(d2), there
was no difference in the value of RMSES (P) between them toidentify the bone location. There were two reasons for thedifference in scattering characteristics between in vivo andwater tank experiments. The ﬁrst was the construction ofmuscle. Muscle tissue is composed of bundles of muscle
ﬁbers with 10–150 μm diameter and covered by fascia.33) In
the present paper, the muscle ﬁbers were simulated by asingle wire. Since the fascia is a plane structure and cannot be
simulated by a wire, the angular amplitude characteristics

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(a1)

(a2)

(b1)

(b2)

(c1)

(c2)

(d1)

(d2)

(e1)

(e2)

Fig. 8. (Color online) Results of applying the RMSE matching method to the human thoracic spine. (a1)–(e1) Subject A, (a2)–(e2) Subject B, (a1), (a2)B-mode image, (b1), (b2) analysis range and bone position, (c1), (c2) the image differentiating the depiction between scatterers and reﬂectors, (d1), (d2) RMSE
values between angular amplitude characteristics obtained at each point and reference scattering characteristics, (e1), (e2) estimated result.

calculated from it may be different from the scatteringcharacteristics of the water tank experiment. Also, the angular
amplitude characteristics from the muscle ﬁbers oriented in
the direction of the long axis of the probe should beconsidered. The second was the wide width of the transmitted
beam relative to the focal area at the shallower region. The
depth of P1(x1, z1) is shallower than that of focus and thus thetransmitted beam was not fully focused. As the beam width

becomes wider, the effect of interference between reﬂected
waves from objects at different locations within the beamwidth becomes larger.
On the other hand, the amplitude angular characteristics
from the bone had a minimum RMSE with the reference dataof f = -8 from Fig. 9(d). The local slope of the bone at the
point P2 (x2 , z2 ) was calculated from the RF signals, and its
value was -8.5, which agreed with the estimated results.

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(a)

(c)

(b)

(d)

Fig. 9. (Color online) Amplitude angular characteristics and the matching results obtained for subject B. (a) The amplitude angular characteristics obtained
for the point P1(x1, z1) in Fig. 8(b2) and the scattering reference data, (b) the RMSE values of R (q; P1) for each reference data, (c) the amplitude angularcharacteristics obtained from the point P2(x 2 , z2 ) in Fig. 8(b2) and the reference data for reﬂection with f = -8, (d) the RMSE values of R (q; P2) for eachreference data.

The angle estimation results of the bone were different in
the depth direction in some parts, although those of theacrylic block were almost constant in the depth direction at
all lateral positions. For example, the angle estimation resultof the bone at the lateral position of 23.0 mm in Fig. 8(e1)showed that the estimation angles at the positions with low
brightness were different from those at the high brightness
positions. Figure 10 shows the relationship between the angle
estimation results and the brightness values of the B-mode
image at the lateral position of 23.0 mm in the depth of 32.6–
33.6 mm in subject A. The red line (−5°) shows theestimated angle at this position from the B-mode image.

The black dotted line shows the acceptable error range, where
we assumed that is within ±3°. At the higher brightness
positions, the angles were estimated as approximately −5°.
However, the angles could not be correctly estimated at thelower brightness positions. A high signal-to-noise ratio
would improve the accuracy of the angle estimation. In the
future, we will further investigate the methods to acquire theaccurate results of the angle estimation.
Differentiation between shallow muscle, especially fascia,
and bone is required to detect the puncture position of theanesthetic needle. To solve this problem, the following
studies are required in the future. (1) Measurements andanalyses of the angular amplitude characteristics from muscle
tissues located shallower than the focal point of the probe, (2)measurements and analyses of the amplitude angular characteristics for a single thin wire and a bundle of multiple
wires, and (3) investigation of the best window function to
calculate the RMSE. The suppression of muscle depiction has
still a challenge, but the proposed method enabled us toemphasize bone depiction.
4. Conclusions

Fig. 10. (Color online) The relationship between the angle estimation
results and the brightness values of the B-mode image at the lateral positionof 23.0 mm in the depth of 32.6–33.6 mm of subject A.

In the present paper, we proposed a depiction method using
the difference in angular amplitude characteristics between
scattering and reﬂection for the sharp depiction of thethoracic spine surface. The normalized cross correlationand the RMSE were used for the matching, and the results
were compared. The use of the RMSE for the matching in thewater-tank experiments allowed us to differentiate theSDDE15-9© 2021 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 60, SDDE15 (2021)

T. Hashimoto et al.

depiction of scattering and reﬂection. In the measurements forhuman thoracic vertebrae, the position and inclination of thebones were almost correctly estimated at the higher brightness
position. To further suppress the depiction of muscle,
weighting functions for calculating RMSE, the angular amplitude characteristics from the scatterers in a shallow region, andthe difference in the angular amplitude characteristics between
the single small scatterer and the aggregate of the multiple
scatterers should be investigated. However, the ability to detect
the reﬂection characteristics from the bone will greatly assist in
thoracic epidural anesthesia in the future.
Acknowledgments
This work was partially supported by JSPS KAKENHI
20H02156.

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