TYPE Brief Research Report
PUBLISHED 07 February 2023
DOI 10.3389/fphy.2023.1077696

OPEN ACCESSEDITED BY

Tadashi Yamaguchi,
Chiba University, Japan
REVIEWED BY

Masaaki Omura,
University of Toyama, Japan
Kazuyo Ito,
Tokyo University of Agriculture andTechnology, Japan*CORRESPONDENCE

Mototaka Arakawa,arakawa@tohoku.ac.jp

In vivo measurement of attenuation
coefﬁcient of blood in a dorsal
hand vein in a frequency range of
10–45MHz: A preliminary study
Mototaka Arakawa 1,2*, Kyohei Higashiyama 1, Shohei Mori 2,
Satoshi Yashiro 3, Yasushi Ishigaki 3 and Hiroshi Kanai 1,2
1
Graduate School of Biomedical Engineering, Tohoku University, Sendai, Japan, 2Graduate School ofEngineering, Tohoku University, Sendai, Japan, 3Division of Diabetes, Metabolism, and Endocrinology,
Department of Internal Medicine, Iwate Medical University, Yahaba, Iwate, Japan

SPECIALTY SECTION

This article was submitted to Medical
Physics and Imaging,a section of the journal
Frontiers in Physics
RECEIVED 23 October 2022
ACCEPTED 25 January 2023
PUBLISHED 07 February 2023
CITATION

Arakawa M, Higashiyama K, Mori S,
Yashiro S, Ishigaki Y and Kanai H (2023), In
vivo measurement of attenuation
coefﬁcient of blood in a dorsal hand vein ina frequency range of 10–45 MHz: A
preliminary study.
Front. Phys. 11:1077696.
doi: 10.3389/fphy.2023.1077696
COPYRIGHT© 2023 Arakawa, Higashiyama, Mori,
Yashiro, Ishigaki and Kanai. This is an openaccess article distributed under the termsof the Creative Commons Attribution
License (CC BY). The use, distribution or
reproduction in other forums is permitted,
provided the original author(s) and the
copyright owner(s) are credited and thatthe original publication in this journal iscited, in accordance with accepted
academic practice. No use, distribution or
reproduction is permitted which does notcomply with these terms.

Frontiers in Physics

In this study, the attenuation coefﬁcient of blood was measured in vivo in thefrequency range of 10–45 MHz. A procedure to correct the distribution of soundpressure in the measurements was discussed. Further, in vivo measurements wereapplied on the dorsal hand vein of four healthy subjects at rest and during
avascularization. As a preliminary result, less variation of the measured
attenuation coefﬁcients was achieved by the proposed method. The comparable
results of the inclination of the attenuation coefﬁcients were obtained at rest andduring avascularization. Furthermore, the attenuation coefﬁcients during
avascularization were markedly higher than those at rest, reﬂecting the degree of
red blood cell aggregation promoted by avascularization. This method may aid in the
non-invasive evaluation of blood properties reﬂecting the degree of red blood cellaggregation.
KEYWORDS

attenuation coefﬁcient, blood, in vivo, red blood cell, avascularization

1 Introduction
Cardiovascular diseases (CVD) are one of the leading causes of death worldwide, andatherosclerosis is the primary factor for CVD development [1] and is closely related to thephysical and chemical properties of blood [2]. Therefore, evaluating blood properties is crucial
for early diagnosis of arteriosclerosis.
The elevation of lipid concentration not only increases the viscosity in blood but also
promotes the progression of atheroma formation [3]. Notably, blood viscosity values are highly
correlated with blood pressure and are higher in patients with hypertension [4] as well as
dyslipidemia and diabetes. By focusing on the propagation of ultrasonic waves in viscoelastic
media, the higher the viscosity, the greater the attenuation coefﬁcient [5]. Therefore, in vivo
non-invasive measurements of the attenuation coefﬁcient of blood are expected to be effective
for screening atherosclerosis.
The attenuation coefﬁcient of human blood has been measured by several researchers[6–18]. However, most of these coefﬁcient values were obtained from sampled blood [6–12,
15, 16, 18]. Moreover, the attenuation coefﬁcients were measured below 10 MHz [6–11, 15],
and the measurements were not conducted around the human body temperature [10, 11,15], or the measurement temperature was not provided [6, 8, 12, 16]. Secomski et al.
measured the attenuation coefﬁcient of blood in vivo [13, 14, 17]. They measured the depth
dependence of the power of a Doppler signal backscattered in a blood vessel. However, as

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2 Methods
2.1 Principle
The experimental setup for measuring the attenuation coefﬁcient
using a high-frequency ultrasonic probe is depicted in Figure 1. The
method in the present study is based on the spectral log difference
method [26, 27]. However, it is difﬁcult to prepare a reference
phantom with a known attenuation coefﬁcient in the frequency
range in the present study. Therefore, the sound pressure property
difference between different depths was corrected by measuring
reﬂection spectra from the ﬂat plate in water [24]. Ultrasonicwaves transmitted from the ultrasound probe propagated throughwater in the membrane and skin and then irradiated the vascularlumen. Waves scattered from the RBCs in the vascular lumen werereceived using the same ultrasonic probe. The power spectrum
Ps (f, di ) of the scattering wave from the vascular lumen at a depth
di is described as

FIGURE 1
Experimental arrangement for the measurement of the attenuation
coefﬁcient of blood. H(f, d) denotes the sound pressure property of theultrasound probe. di is the depth from the probe surface. dw , dsk , and dbi
are the length of water, skin, and blood, respectively.

2
Ps f, di   Sf Xf Gf Hf, di  Af, 0: di  ,where S(f) denotes the backscattering property of RBCs, X(f)denotes the frequency characteristic of the applied signal, G(f)denotes the transmitting and receiving characteristics of theultrasound probe, H(f, di ) denotes the sound pressure propertyof the ultrasound probe at a depth di , A(f, 0: di ) denotes theattenuation property of the round-trip propagation path between
the probe (d  0) and a point at depth di , and f denotes thefrequency. H(f, di ) also includes the transmission losses atthe boundaries between water and the skin and between the skinand the blood vessel. A(f, 0: di ) is caused by scattering andabsorption.
In our experiment, we set two points along an ultrasonic beam at
depths di and ds in the lumen of a blood vessel to obtain theattenuation property of blood between the two points, where ds
was set as the starting point. By assuming that S(f), X(f), andG(f) do not depend on the depth di or ds , the following relationshipholds:
2 
2
Ps f, di  Hf, di  Af, 0: di  (2)2 · .
Ps f, ds  Hf, ds  Af, 0: ds 2the objective of their study was to determine the level of hematocrit,the measurement results at 16 and 20 MHz [13] or only 20 MHz[14, 17] were used considering the sensitivity of their experimental
system to the hematocrit level of blood. Therefore, the frequency
dependence of the attenuation coefﬁcient of blood in vivo was notdiscussed.
We have been studying methods for evaluating the size of red
blood cell (RBC) aggregates by analyzing the scattering power
spectrum obtained via ultrasonic backscattering measurementsof RBCs [19–24]. Notably, the backscattering power obtained
from a single sphere signiﬁcantly depends on the frequency foreach aggregate size [25], and the larger the diameter of a sphere, thesmaller the slope of the frequency dependence of the power
spectrum. The size of RBC aggregates is estimated by ﬁtting theslope of the measured power spectrum to that of a single scattering
sphere’s theoretically obtained scattering characteristics. To extract
the scattering property from RBC aggregates, the power spectrum
obtained from the vascular lumen is normalized by that obtained
from the posterior wall of a blood vessel [20–23] or compared withthe reference scattering spectrum [24]. To estimate the size of RBC
aggregates with greater accuracy, the attenuation coefﬁcients of theskin and blood must be measured, and the attenuation property
differences between the two power spectra must be corrected[22–24]. To measure the attenuation coefﬁcient, power spectra
at only two different depths were used. Then, there was a problem
that the variation of the measured attenuation coefﬁcients waslarge.
In the present study, ﬁrst, a procedure to correct the distribution ofsound pressure in the measurements was discussed. Furthermore, as apreliminary study, we non-invasively measured the attenuation
coefﬁcient of blood in a dorsal hand vein in the frequency range of
10–45 MHz at rest and during avascularization for four subjects toshow the possibility for an evaluation method of the blood property. A
procedure to robustly measure the attenuation coefﬁcient of blood wasexperimentally discussed.

Frontiers in Physics(1)

As illustrated in Figure 1, because the acoustic path is approximately
divided into a path in water with a propagation length dw , a path in theskin with a propagation length dsk , and a path in the blood in a vessel,
the attenuation property |A(f, 0: di )| is expressed as the product ofthat in water |Aw (f, 0: dw )|, that in skin |Ask (f, dw : (dw + dsk))|, andthat in blood |Ab (f, (dw + dsk): (dw + dsk + dbi)|, as follows:

 
Af, di   Aw f, 0: dw  · Ask f, dw : (dw + dsk (3)· Ab f, (dw + dsk): (dw + dsk + dbi,
where dbi denotes the distance from the anterior wall to the depth di in
the blood vessel.
Let us assume that the attenuation property |A(f, 0: di )|2 can bemodeled using the attenuation coefﬁcient of the medium, α(f), as
follows:
Af, 0: di 2  e−4di α(f) .

(4)

By applying Eq. 4 to Eq. 3, the following equation can be derived:

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FIGURE 2
B-mode images of the dorsal hand vein (A) at rest and (B) during avascularization.

Af, 0: di 2  e−4dw αw (f)−4dsk αsk (f)−4dbi αb (f) ,where ΔAw (f, Δd) denote the attenuation properties in water at a
distance Δd di − ds . Using Eq. 4, ΔAw (f, Δd) can be calculated asfollows:
ΔAw f, Δd2  e−4Δd αw (f) ,
(10)

(5)

where αw (f), αsk (f), and αb (f) denote the attenuation coefﬁcientsof water, skin, and blood, respectively. When di is close to ds andthey include the same transmission losses, by substituting Eq. 5
into Eq. 2, the following relationship can be derived because theattenuation properties in water and skin are canceled:2
Ps f, di  Hf, di  · exp−4αb f(dbi − dbs )
Ps f, ds  Hf, dr 2(6)
Hf, di 2 
 · exp−4αb fΔd,
Hf, ds 2

where αw (f) can be determined in advance based on publisheddata [28].
By substituting Eqs 9, 10 into Eq. 7, we can obtain the attenuation
coefﬁcient αb (f) by correcting the effect of the ratio of the soundpressure properties |H(f, di )|2 /|H(f, ds )|2 , as follows:
αb f 

where Δd  dbi − dbs  di − ds , that is, the distance between the depth
di and depth ds of the starting point, where di is the different depthwith ds . Based on Eq. 6, the attenuation coefﬁcient αb (f) of blood canbe derived as follows:Hf, ds 2
1 ⎡⎢⎣ Ps f, ds αb f ln
(7)
 − ln 
2 ⎤⎥⎦.
Hf, di 
4Δd
Ps f, di where P′s (f, di ) is deﬁned by2
PR f, ds  P′s f, di   Ps f, di  · 
·ΔAw f, ΔdPR f, di PR f, ds 
 Ps f, di  · 
 · e−4Δd αw (f) .
PR f, di 

(12)This denotes the power spectrum whose sound property H(f, di ) iscorrected by the sound pressure property H(f, ds ) at the starting
depth ds based on the attenuation property difference in water|ΔAw (f, Δd)|2 . Thus, the corrected power spectrum P′s (f, di ) isdifferent from Ps (f, ds ) only by the attenuation property differencein blood |ΔAb (f, Δd)|2 , which is caused by the difference Δd in depth.
Therefore, the procedure for estimating the attenuation coefﬁcient
αb (f) is as follows: In advance, the power spectra PR (f, di ) andPR (f, ds ) are obtained by measuring the radiofrequency (RF) signals
reﬂected from the surface of a ﬂat plate set at two depths di and ds inwater, respectively. Following this, for in vivo measurements, thepower spectra Ps (f, di ) and Ps (f, ds ) are obtained by measuring
the RF signals scattered from blood at depths di and ds in the vascularlumen, respectively. The attenuation property in water |ΔAw (f, Δd)|2
is determined based on Eq. 10. By substituting these values into Eq. 12,
the corrected power spectrum P′s (f, di ) can be determined, and theattenuation coefﬁcient of blood, αb (f), given in Eq. 11, is estimated.

(8)

where R denotes the reﬂection coefﬁcient from water to theﬂat plate, and we can assume that it does not depend on thefrequency. Similar to Eq. 2, by assuming that R, X(f), and G(f)do not depend on the depth di or ds , the following relationshipholds:

Hf, di 2PR f, di 
1
(9)
 

 
,
Hf, ds 2PR f, ds  ΔAw f, Δd2

Frontiers in Physics

1
Ps f, ds 
ln ′
,
4Δd
Ps f, di (11)Thus, to determine αb (f), we must eliminate the second term on
the right-hand side of Eq. 7, that is, the ratio of the sound pressure
property up to the depth di to that up to ds , |H(f, di )|2 /|H(f, ds )|2 .
In our analysis, the term |H(f, di )|2 /|H(f, ds )|2 was determined inadvance using the power spectra PR (f, di ) and PR (f, ds ) of the
waves reﬂected from the surface of a ﬂat plate set at different depths
di and ds in water, respectively [24].
As well as Eq. 1, the power spectrum PR (f, d) at depth d in water
can be expressed as follows:2
PR f, d  R Xf Gf Hf, d Aw f, 0: d ,2
1
Ps f, ds PR f, ds   − lnΔAw f, Δd ln
4ΔdPs f, di PR f, di 

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FIGURE 3
Power spectra measured at different depths in the vascular lumen (A) at rest and (B) during avascularization and depth dependence of the power received
from the vascular lumen at 20, 30, and 40 MHz (C) at rest and (D) during avascularization. The solid lines in (C) and (D) are the linearly approximated line.

The robustness of the attenuation coefﬁcient αb (f) given in Eq. 11
is conﬁrmed by measuring the power spectra at multiple sets {di , ds } of
different depths.

Graduate School of Engineering, Tohoku University, and all theparticipants agreed to participate in the present study. RF signals
scattered from the lumen were obtained using ultrasonic short-axis
measurements [29]. The focal depth dF of the probe was set at thecenter of the lumen. In addition to the measurements conducted atrest, RF signals were acquired after avascularization of the dorsal
hand vein using crucible scissors [24]. By pressing two points on
the ﬁngertip and heart sides, the blood ﬂow was stopped upstream,
and the backﬂow of blood was avoided downstream. Notably, RBC
aggregation is more likely to occur in the lumen between the twopoints under low shear rates.
Data for ﬁve frames were acquired every 10 s for control from 0 s
to 60 s, avascularization was applied immediately after themeasurement at 60 s, and data for 13 frames were acquired for
70–190 s every 10 s. RF data along 15 beams passing through thecenter of the vascular lumen were used in each frame. The power
spectrum was obtained by windowing the RF signals using a Hanningwindow with a length of 0.15 μs at each depth di ; following this, thepower spectra obtained for the 15 beams for ﬁve frames were averaged
to obtain the power spectrum Ps (f, di ) at each time instant for each
depth di . Here, ds was set at 8.7 mm around a focal depth of 8.75 mm.
Seven power spectra Ps (f, di ) were averaged from 0 to 60 s for thecontrol, and seven power spectra Ps (f, di ) were averaged from 130 to
190 s for the data acquired during avascularization because theaggregation state stabilized within 1 min after avascularization [30].

2.2 In vivo experiments
A high-frequency ultrasound system (Tomey UD-8000) was used
for subsequent in vivo experiments. The sampling frequency was
240 MHz. A mechanical scanning linear probe comprising aconcave transducer with an operating central frequency of 30 MHz(frequency range: 19–40 MHz) was connected to the ultrasoundsystem. The focal length of the probe dF was 8.75 mm.
Prior to the in vivo measurement, the sound pressure |H(f, d)|2of the ultrasound probe was measured by setting a ﬂat silicone
rubber plate at depth d; this was perpendicular to the beam
direction of the ultrasound probe in water. The RF signals
reﬂected from the ﬂat plate were measured by changing thedepth d of the plate with a 0.1 mm interval around the focal
depth dF of the probe.
As a preliminary study, in vivo measurements were applied on
the dorsal hand vein of four healthy subjects A, B, C, and D for 20 s.
The diameters of the dorsal hand vein (approximately 2–3 mm)
were much larger than the wavelength (51 μm at 30 MHz). These
measurements were approved by the Ethics Committee of the

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FIGURE 4
Attenuation coefﬁcients of blood at rest and during avascularization. (A) Subject A, solid lines: measured results using power spectra from 8.1 mm to
8.9 mm at 0.1 mm intervals, dashed lines: linearly approximated lines; (B,C) at rest and during avascularization for subject A, respectively, black line: obtainedusing power spectra from 8.1 mm to 8.9 mm at 0.1 mm intervals, red, blue, and green lines: obtained from power spectra at two depths {8.1 mm and 8.9 mm},{8.2 mm and 8.8 mm}, and {8.3 mm and 8.7 mm}, respectively; (D,E) at rest and during avascularization for subject A, respectively, black line: obtainedusing seven frames, the other lines: obtained from power spectra with each frame from 0 to 60 s and from 130 to 190 s; (F) subjects A (black), B (red), C (blue),and D (green), solid lines: at rest, dashed lines: during avascularization.

3 Results

range of 10–45 MHz. The attenuation coefﬁcients at rest,
αrest (f), and during avascularization, αava (f), were αrest (f) 
0.178 f [MHz] − 1.04 [dB/mm] and αava (f)  0.158 f [MHz] +0.56 [dB/mm] at 10–45 MHz, respectively. Thus, αava (f) is
greater than αrest (f) by approximately 1.1 dB. The scattering
power increased owing to avascularization, as depicted in
Figure 2 [19–24]. Using the method proposed in the present
study, we could non-invasively observe that the increase in thebackscattering component reduced the propagation component as
the increase of attenuation coefﬁcient. We obtained theattenuation coefﬁcients from the power spectra at the following
pairs of two depths {8.1 mm and 8.9 mm}, {8.2 mm and 8.8 mm},and {8.3 mm and 8.7 mm}. The results are shown in Figures 4B, C
with the data obtained from 8.1 mm to 8.9 mm at 0.1 mm intervals
at rest and during avascularization, respectively. The root-meansquare errors in ﬁtting a linear line to the measured attenuation
coefﬁcients were 0.21 (dB/mm) and 0.14 (dB/mm) for {8.1 mm
and 8.9 mm}, 0.28 (dB/mm) and 0.26 (dB/mm) for {8.2 mm and
8.8 mm}, and 0.54 (dB/mm) and 0.32 (dB/mm) for {8.3 mm and8.7 mm}, at rest and during avascularization, respectively. In
contrast, those were 0.17 (dB/mm) and 0.13 (dB/mm) for thedata obtained from 8.1 mm to 8.9 mm at 0.1 mm intervals, at
rest and during avascularization, respectively. By setting many
analysis points, the variations of the measured attenuation
coefﬁcients to the linear line were reduced. Next, we obtained

Figures 2A, B depict ultrasonic short-axis B-mode images of thevascular lumen in the dorsal hand vein at rest and during
avascularization for subject A, respectively. The lumen
brightness in Figure 2B appears higher than that in Figure 2A
owing to the increased scattering power caused by RBC
aggregation. As illustrated in each B-mode image, the central
depths {di } of the analysis windows of the RF signals were set
from 8.1 mm to 8.9 mm at 0.1 mm intervals.
Figures 3A, B present the corrected power spectra P′s (f, di )obtained from Eq. 12. The corrected power spectra P′s (f, di )during avascularization (Figure 3B) were larger than those at rest
(Figure 3A). Figures 3C, D depict the depth dependence of thecorrected received power P′s (f, di ) for signals scattered from theblood vessel at 20, 30, and 40 MHz at rest and during
avascularization, respectively. The corrected received power
P′s (f, di ) decreased almost linearly as the depth d increased, andthe power change increased with the frequency f.
Using Eq. 11, the attenuation coefﬁcient α(f) of blood wasestimated with the data obtained from 8.1 mm to 8.9 mm at
0.1 mm intervals at rest and during avascularization, and theresults for subject A are presented in Figure 4A. The
attenuation coefﬁcients α(f) both at rest and during
avascularization increased almost linearly in the frequency

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18]. In contrast, there is no blood ﬂow during avascularization, andthere is no effect on the attenuation coefﬁcient by the blood ﬂow.
Therefore, the effect of the blood ﬂow did not change the magnituderelationship of the attenuation coefﬁcients at rest and during
avascularization.
In contrast, αava (f) were markedly greater than αrest (f) for four
subjects, as presented in Figure 4D. The relative relationship between
them is correct even if the ratio of the sound pressure properties|H(f, di )|2 /|H(f, ds )|2 has an error because the same ratio is
employed for the correction as the analysis range is the same atrest and during avascularization. Therefore, the proposed method
demonstrates the potential to non-invasively evaluate blood
properties, reﬂecting the degree of RBC aggregation.
To correct the ratio of the sound pressure properties, a ﬂat plate
was used as a reﬂector. The analysis was based on the plane wave
model. In contrast, a mechanical scanning linear probe comprising aconcave transducer was used. Therefore, aberration could also affectthe result. The effect will be discussed in the future by a simulation
experiment or an experimental investigation using a reference
phantom whose attenuation coefﬁcient is measured by the pulse
transmission method.

the attenuation coefﬁcient from the power spectrum with eachframe from 0 to 60 s and from 130 to 190 s from 8.1 mm to 8.9 mm
at 0.1 mm intervals. The results are shown in Figures 4D, E at restand during avascularization, respectively. Averaging seven frames
reduced the variations, and it clariﬁed the difference inattenuation coefﬁcients between at rest and during
avascularization. From Figures 4B–E, the improvement of therobustness in the attenuation coefﬁcient measurement was
conﬁrmed. Figure 4F shows the attenuation coefﬁcients for four
subjects A, B, C, and D. The attenuation coefﬁcients were different
for each subject. However, the attenuation coefﬁcients during
avascularization, αava (f), were larger than those at rest, αrest (f)for all subjects.

4 Discussion
As shown in Figures 4B, C, the improvement of the robustnessof the measured attenuation coefﬁcients was conﬁrmed by setting
plural analysis depths. In this study, the analysis points were set
from 8.1 to 8.9 mm at 0.1-mm intervals. It is difﬁcult to expand theanalysis region because of the signal-to-noise ratio of the received
signals and the size of the blood vessel. To increase the analysis
points, it is necessary to shorten the interval. In contrast, measured
attenuation coefﬁcients differed at each frame from Figures 4D, E.
Therefore, the discussion of the relationship between measurement
accuracy and the number of analysis points is necessary for our
future work.
The attenuation coefﬁcients for four subjects A-D were
2.5–4.8 dB/mm at rest and 3.9–5.3 dB/mm during avascularization
at 30 MHz. The attenuation coefﬁcients in blood strongly depend on
the hematocrit level [17]. Therefore, the attenuation coefﬁcientdifferences among subjects could be caused by the differences inblood properties. The relationship between the attenuation
coefﬁcients and blood properties will be investigated in the future.
The average attenuation coefﬁcients at rest, αrest (f), for four
subjects were 2.0 dB/mm at 20 MHz and 3.8 dB/mm at 30 MHz.
Previous literature reports these values to be 1.6 dB/mm [12] and1.2 dB/mm [18] at 30 MHz for sampled blood, and 0.6–0.9 dB/mm
at 20 MHz based on in vivo measurements depending on
hematocrit levels of 32.0%–49.3% [17]. The attenuation
coefﬁcient measured herein is larger than that reported in theliterature. This increase could be caused by the incomplete
correction of the ratio of sound pressure properties|H(f, di )|2 /|H(f, ds )|2 because the propagation media differed
between water in the ﬂat plate measurement and blood and skinin the in vivo measurement.
There is blood ﬂow in vivo. Laminar ﬂow is assumed in the dorsal
hand vein. Then, the blood velocities are the highest in the center ofthe blood vessel and the lowest near the anterior and posterior walls inthe depth direction. The lowest velocity might cause red blood cellaggregation as well as during avascularization because of the low shear
rate. In the present study, the focal point of the probe (dF = 8.75 mm)
was set at the center of the lumen. Therefore, the slight scattering
property distribution might occur, that is, larger scattering in theshallower position, and it decreased as a larger depth around the focal
point. Then, it might cause an apparent larger attenuation coefﬁcient.
Therefore, it might also be one of the reasons that the measured
attenuation coefﬁcient became larger than those in the Refs. [12, 17,

Frontiers in Physics

5 Conclusion
In this study, the attenuation coefﬁcient of blood was measured
in vivo at 10–45 MHz at rest and during avascularization. For this,the differences in sound pressure properties among several
measurement points were measured using a ﬂat plate placed inwater in advance, and the values were used for correction. In vivo
measurements were applied in the dorsal hand vein of four healthy
subjects. As a preliminary result, less variation of the measured
attenuation coefﬁcients was achieved by the proposed method. The
comparable results of the inclination of the attenuation coefﬁcientswere obtained at rest and during avascularization. Furthermore,
the attenuation coefﬁcient during avascularization αava (f) was
found to be markedly greater than that at rest αrest (f), primarily
owing to RBC aggregation. Thus, the usefulness of thismeasurement method was successfully demonstrated.
Hereafter, we aim to improve our evaluation of sound properties,
including the effect of different media, and we aim to include othersubjects, such as arteriosclerosis patients, to demonstrate theusefulness of the non-invasive method for evaluating blood properties.

Data availability statement
The original contributions presented in the study are included in
the article/supplementary material, further inquiries can be directed tothe corresponding author.

Ethics statement
The studies involving human participants were reviewed andapproved by Ethics committee concerning medical research
involving humans Graduate School of Engineering, Tohoku
University. The patients/participants provided their written
informed consent to participate in this study.

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Author contributions

Conﬂict of interest

Study design, data processing, interpretation of data, andmanuscript writing, MA; experimental work and data processing,
KH; study support and interpretation of data, SM; study support,
SY; study support and manuscript review, YI; study design,interpretation of data, and manuscript review, HK. All Authors
have read the manuscript and agreed to the published version of
the manuscript.

The authors declare that the research was conducted in theabsence of any commercial or ﬁnancial relationships that could beconstrued as a potential conﬂict of interest.

Publisher’s noteAll claims expressed in this article are solely those of the authorsand do not necessarily represent those of their afﬁliated organizations,or those of the publisher, the editors and the reviewers. Any productthat may be evaluated in this article, or claim that may be made by its
manufacturer, is not guaranteed or endorsed by the publisher.

Funding
This work was partially supported by JSPS KAKENHI 21H03835.

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