Journal of Medical Ultrasonics (2021) 48:3–12
https://doi.org/10.1007/s10396-020-01065-z

ORIGINAL ARTICLE–PHYSICS & ENGINEERING

Evaluation method of the degree of red blood cell aggregationconsidering ultrasonic propagation attenuation by analyzing
ultrasonic backscattering properties
Kanta Nagasawa1 · Akiyo Fukase1 · Shohei Mori2
Hiroshi Kanai1,2· Mototaka Arakawa1,2· Satoshi Yashiro3 · Yasushi Ishigaki3 ·Received: 21 February 2020 / Accepted: 13 October 2020 / Published online: 12 January 2021
© The Japan Society of Ultrasonics in Medicine 2021

Abstract
Purpose Red blood cell (RBC) aggregation is one of the main factors that determines blood viscosity and an important
indicator for evaluating blood properties. As a noninvasive and quantitative method for diagnosing blood properties, ourresearch group estimated the size of RBC aggregates by fitting the scattered power spectrum from the blood vessel lumen
with the theoretical scattering characteristics to evaluate the degree of RBC aggregation. However, it was assumed that the
propagation attenuation of ultrasound in the vascular lumen was the same regardless of whether RBCs were aggregated ornot, which caused systematic errors in the estimated size.
Methods To improve the size estimation accuracy, we calculated and corrected the attenuation of the blood vessel lumen
during RBC aggregation and non-aggregation. The attenuation in the blood vessel lumen was calculated with the spectra
acquired from two different depths.
Results In the basic experiments using microparticles, the estimation accuracy decreased as the concentration increased in
the case of the conventional method, but the estimated size tended to approach the true size irrespective of the concentration, removing the propagation attenuation component with the proposed method. In the in vivo experiment on the human
hand dorsal vein, the size was estimated to be larger during RBC aggregation and smaller during non-aggregation using the
proposed method.
Conclusion These results suggest that the proposed method can provide precise size estimation by considering the propagation
attenuation component regardless of differences in blood conditions such as RBC concentration and degree of aggregation.
Keywords Ultrasound scattering · Red blood cells · Aggregation · Attenuation

Introduction
Evaluation of blood properties is useful for early detectionof cardiovascular diseases, and one of the main indicators isthe degree of red blood cell (RBC) aggregation [1, 2]. RBC* Mototaka Arakawa
arakawa@ecei.tohoku.ac.jp
1

Graduate School of Biomedical Engineering, Tohoku
University, Sendai 980‑8579, Japan

2

Graduate School of Engineering, Tohoku University,
Sendai 980‑8579, Japan

3

Division of Diabetes, Metabolism and Endocrinology,
Department of Internal Medicine, Iwate Medical University,
Yahaba, Iwate 028‑3695, Japanaggregation is a reversible phenomenon among RBCs, and
it is likely to occur when the blood flow is at a low shear
rate. The degree of RBC aggregation is one of the factorsthat determines blood viscosity, and it has been reported
to be related to other blood properties [3]. Conventional
evaluation methods of blood properties are mainly basedon the sampling of blood, which is invasive. Therefore, wehave investigated a noninvasive and quantitative evaluation method of the blood properties based on calculating
the degree of aggregation from the scattering properties of
RBCs using ultrasound. RBCs are the main component ofblood. There have been several reports on the evaluation of
scattering properties from RBCs [4, 5]. Several studies havebeen reported on the evaluation of blood properties using
ultrasound. Shung et al. observed changes in the brightnessof blood echoes during a cardiac cycle [6, 7], and Patat et al.

13Vol.:(0123456789)

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observed sound velocity and scatterer size changes during
blood coagulation using human whole blood in vitro [8, 9].
All of these evaluation methods were applied to blood drawnby blood sampling, so these are invasive.
As a noninvasive method, in our research group, Saito
et al. regarded the aggregated RBCs as a sphere scatterer
in in vivo measurements, estimated the scatterer size by
analyzing ultrasound scattering properties, and evaluatedthe degree of RBC aggregation [10, 11]. Kurokawa et al.
proposed a selection of analysis beams in the detection ofreflected waves from the posterior wall of a blood vessel,
thereby improving the reproducibility of the reflected spectrum [12]. They also confirmed a clear difference in theestimated size before and during avascularization in in vivo
measurements. However, the difference in the propagation
attenuation component due to the difference in the ultrasonicpropagation paths between the acquisitions of the power
spectra from the lumen and the back wall of the blood vessel as a reference was not considered in their method. This
caused a systematic error in the size estimation results. In
fact, the deterioration of the estimation accuracy was confirmed as the particle size and the particle concentration
increased in the basic experiments using microparticles.
There are individual differences from 30 to 50% in the hematocrit (volume ratio of RBCs in the blood) [13], so it is necessary to consider the propagation attenuation component.
There have been several reports on the measurement ofpropagation attenuation in vivo. In the time domain, Baldwin et al. estimated myocardial attenuation using M-mode
images [14], and Chen et al. estimated liver attenuation
using harmonic imaging (HMI) [15]. In the frequency
domain, there are estimation methods of attenuation using
the downshift of the center frequency and the spectral difference [16]. Heo et al. estimated the attenuation of soft
tissues by calculating the block power spectrum [17]. Kucet al. estimated the attenuation using the difference in theslope of the logarithmic power spectra for two echo signals
obtained from different depths in a tissue [18].
In the present study, we derived intravascular ultrasoundpropagation attenuation to estimate the size of RBCs in
consideration of ultrasound propagation attenuation. Furthermore, we attempted to improve the accuracy of the size
estimation method by correcting the propagation attenuation
components.

Materials and methods
Measurement of ultrasonic backscatter properties
When the scatterer size is sufficiently smaller than the wavelength of the incident ultrasound, the scattering property
follows Rayleigh scattering, and the scattering power is

13

Journal of Medical Ultrasonics (2021) 48:3–12

proportional to the fourth power of the frequency. As thescatterer size increases, the frequency dependence of thescattered power becomes smaller.
Figure 1a, b shows the schematic diagrams of acquisitionof RF signals scatteredfrom
RBCs to obtain the scattered()
power spectrum Ps f , d0 and those reflected from a posterior( wall) of the vein to obtain the reflected power spectrum
Pr f , d0 , respectively. f is the frequency and d0 is the distance from the probe to the data acquisition position. Ultrasound is transmitted to blood vessels through water, gel, andepidermis. The focal point of the ultrasonic probe was set on
the center of the vessel lumen in Fig. 1a and on the posteriorwall of the vessel in(Fig. )1b. Equations (1) and (2) show
the power spectra Ps f , d0 scattered( from) the RBCs in thelumen of the blood vessel and Pr f , d0 reflected from theposterior wall of the vein, respectively. The measurement
positions of both spectra are set at the same distancefrom()
the probe so that the sound pressure properties H f , d0 are
equal:

(
) | (
)
(
) (
)
|2
Ps f , d0 = |S f , d0 G(f )AS f , d0 H f , d0 X(f )| ,
|
|

(1)

(
) |
(
) (
)
|2
Pr f , d0 = |R ⋅ G(f )Ar f , d0 H f , d0 X(f )| .
|
|

(2)

In( addition
to the scattering property from the (RBCs))
S f , d0 , the scattered power spectrum from RBCs Ps f , d0
includes the transmission/reception property of the transducer G(f( ), the) sound pressure property of the ultrasonicprobe H f , d0 , the frequency property of the applied(signal)X(f( ) , andAs (f , d0 ).
( property)) the propagation( attenuation)
Pr f , d0 includes R and Ar f , d0 , not S f , d0 and AS f , d0 ,respectively. R represents the reflection coefficient from theposterior wall of(the bloodvessel,( and)) it has no frequency
dependence. Ar f , d0 and AS f , d0 are the propagation
attenuation properties when acquiring the scattered wave
from the RBC and the reflected wave from the back wall of
the blood vessel, respectively.
()
only the required scattering property S (f , d0 ),(To extract)
Ps f , d0 is normalized by the reflected spectrum Pr f , d0from a posterior wall of the vein, as shown in the following
equation:
)
(
) (
)
(
)
| (
|2
|S f , d0 G(f )AS f , d0 H f , d0 X(f )|Ps f , d0||
10 log10 () = 10 log10
(
) (
)
|2
|
Pr f , d0|R ⋅ G(f )Ar f , d0 H f , d0 X(f )|
|
|
)|2
)|2
| (
| (
|AS f , d0 ||S f , d0 ||| + 10 log |≈ 10 log10 |
10
)|2 .
| (
|R|2
A
f
,
d
| r
0 ||
|

(3)
)
Since the sound pressure property H f , d0 , the applied signal X(f ), and the transmission/reception characteristic G(f )(Journal of Medical Ultrasonics (2021) 48:3–12

5Fig. 1  Schematic diagrams ofacquisitions of RF signals when
acquiring scattered or reflected
waves. a Ps (f , d0 ) from thelumen( (before) avascularization).
b Pr( f , d0) from the rear wall.
c P(a f , d)1 from depth d1. d
Pa f , d2 from depth d2

are equal, these components are canceled by the normalization shown in Eq. (3). Furthermore, for the conventional
method [10–12], the attenuation in each measurement inFig.
to be equal, which means( 1a,) b was( assumed)
AS f , d0 = Ar f , d0 , and the second term on the right sideof Eq(. ( 2 ) wa s c o)nsidered to be 0. Then,
)|2
| (
2
was obtained from
10 log10 |S f , d0 | ∕|R|
|
|
{ (
) (
)}
10 log10 Ps f , d0 ∕Pr f , d0 . However, the focal positionsin the two measurements are different. Therefore, the intravascular ultrasound propagation paths are different fromeach other, as shown in Fig. 1a, b, and it is considered thatthe above assumption is not strict. Aw (f , d), Ag (f , d), As (f , d),and Ab (f , d) are the attenuation properties of propagation inwater, ultrasonic gel, skin, and blood before avascularization, respectively. In general, the propagation attenuation
property A(f , d) can be expressed as A(f , d) = e−2𝛼(f )d withthe attenuation coefficient 𝛼(f ) and the propagation distanced.
The propagation paths in water, ultrasonic gel, skin, andblood vessels when acquiring scattered waves from RBCs
are dw , dg , ds, and db, respectively. The attenuation compo)|2
)|2
| (
| (
nents |As f , d0 | and |Ar f , d0 | are represented as Eqs. (4)||||and (5), respectively, as the sum of the attenuation components in water, gel, skin, and the lumen of the blood vessel:)|2 | (
) (
) (
) (
)|2
| (
|AS f , d0 | = |Aw f , dw Ag f , dg As f , ds Ab f , db | , (4)
|
|
|
|
)|2
| (
|Ar f , d0 |
|
|
) (
) (
) (
)|2
| (
= |Aw f , dw − db + dg ∕2 Ag f , dg ∕2 As f , ds Ab f , 2db | .
|
|

(5)

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Journal of Medical Ultrasonics (2021) 48:3–12

When the reflected wave from the posterior wall is acquired,
the propagation distance in the blood vessel is twice thatwhen the scattered wave from the lumen is acquired, but the
propagation distances in water and gel are shortened accordingly. Therefore, the total propagation distance d0 is equal in
the two measurements. The propagation attenuation compo)|2 | ()|2| (nent 10 log10 |AS f , d0 | ∕|Ar f , d0 | of the second term on| |||the right side of Eq. (3) is obtained as follows:)|2| (|AS f , d0 ||| = 10 log |A (f , d )|2 − 10 log |A (f , d )|2
10 log10 (
0 ||
0 ||
10 || S
10 || r)|2|
|Ar f , d0 |
|
|
]
[
}
{
} dg {𝛼 (f ) − 𝛼g (f ) ,= 17.37 db 𝛼b (f ) − 𝛼w (f ) +
2 w

(6)

where 𝛼b (f ) is the attenuation coefficient of blood before
avascularization and 𝛼w (f ) is the attenuation coefficient ofwater. We insert the measured distance from the B-mode
i m a g e i n t o db a n d t h e p u b l i s h e d d a t a
𝛼w (f ) = 1.94 × 10−16 × f 2 (dB∕mm) (at 23 ℃) [19] into 𝛼w (f ).
𝛼g (f ) is the attenuation coefficient of gel. It is calculated fromthe difference in the amplitude spectra of the reflected waves
from the same phantom when the medium of the ultrasonicwave propagation paths are changed with water and gel,referring to the published data of 𝛼w (f ) [19]. Therefore, if
the attenuation coefficient 𝛼b (f ) of the blood can be obtained,
the propagation attenuation component)|2 | ()|2| (10 log10 |AS f , d0 | ∕|Ar f , d0 | that occurred during nor| |||malization in Eq. (3) can be calculated and removed.

Calculation( of) blood attenuation coefficient()˛𝐛 f , ˛𝐛 ′ f
To calculate the attenuation coefficients of blood before
avascularizaition ( 𝛼b (f ) ) and during avascularization�(𝛼b (f )), we consider calculating the power spectra from different depths d1 and d2(d1 < d0 < d2 , d0 ∶ focus), as shownin Fig. 1c, d. d1 and d2 are made an equal distance from thecenter of the lumen to reduce the difference in the RBC
aggregation sizes caused by the distribution of the bloodflow velocity. In these figures, the propagation paths in bloodvessels are set as db1 and db2, respectively. The power spectra
obtained from each depth can be expressed as Eqs. (7) and
(8):

(
) | (
)
(
) (
)
|2
Pa f , d1 = |S f , d1 G(f )A f , d1 H f , d1 X(f )| ,
|
|

(7)

(
) | (
)
(
) (
)
|2
Pa f , d2 = |S f , d2 G(f )A f , d2 H f , d2 X(f )| .
|
|

(8)

Here, assuming that the shear velocities at the positions of d1
and d2 are the same, because the positions are made an equal

13

(
(
)
)
distance from the center of the lumen, S f , d1 and S f , d2
are treated as the same. Taking the ratio of these two spectra
and the logarithm gives the following equation:
)|2
)|2
(
)
| (
| (
|A f , d1 ||H f , d1 |Pa f , d1||||
10 log10 () = 10 log10 ()|2 + 10 log10 | ()|2 .
|Pa f , d2|A f , d2 ||H f , d2 |
|
|
|
|

(9)

Equation (9) is converted into the following equation:
)|2
)|2
(
)
| (
| (
|A f , d1 ||H f , d1 |
P
f
,
d
a
1
|
|
|
10 log10 | ()|2 = 10 log10 P (f , d ) − 10 log10 | (
)|2 .
|
a
2
|A f , d2 ||H f , d2 |
|
|
|
|

(10)

T h e s o u n d p re s s u re p ro p e r t y d i f fe re n c e)|2 | ()|2
| (10log10 |H f , d1 | ∕|H f , d2 | between the distances d1 and| |||d2 in the second term on the right side of Eq. (10) is derived
from the reflected waves from the underwater phantom andcorrected.
property difference)( Therefore, the attenuation)|2)|2 | (
| (10log10 |A f , d1 | ∕|A f , d2 | can be obtained by meas|
| |
|
(
(
)
)
uring Pa f , d1 and Pa f , d2 . The left side of Eq. (10) canbe expressed as follows:

)|2
)|2
| (
| (
|A f , d1 ||Ab f , db1 ||||10 log10 | ()|2 = 10 log10 | ()|2||A f , d2 ||Ab f , db2 |
|
| (
(|
)
)|
= 20{log10 Ab f , db1 − log10 Ab f , db2 }= 20{log10 e−2𝛼b (f )db1 − log10 e−2𝛼b (f )db2 }()= 17.37 db2 − db1 𝛼b (f ).

(11)

Therefore, the attenuation coefficient of blood 𝛼̂b (f ) is
obtained by the following equation:)|2| (|A f , d1 |
1
| .
|
𝛼̂
(
) ⋅ 10 log10 (b (f ) =)|2|
17.37 db2 − db1|A f , d2 |
|
|

(12)

Here, the propagation attenuation is caused by two factors,i.e., scattering and absorption. The attenuation coefficient�
of blood during avascularization (𝛼b (f )) can be calculated
in the same way.

Size estimation method by fitting theoreticaland measured properties
In the present study, a scatterer was modeled by assuming an
infinite number of infinitesimal point sources on the surface
of a spherical scattering source [20]. The theoretical scattering property when the scatterer is irradiated by a plane
wave is given by [21]

Journal of Medical Ultrasonics (2021) 48:3–12∞]
Q(ka) ∑ 2n + 1 2 [ �=sin 𝛿n (ka) ,224𝜋an=0 (ka)7(13)

where Q(ka) is the scattering cross-section, k is the wavenumber, a is the radius of the scatterer, n is the number of�point sources on the surface of the scatterer, and 𝛿n (ka) isthe derivative of the phase difference between the incident
and scattered waves.
Obtaining a theoretical power that minimizes the sumof squares 𝜀(a, b) of the difference between the normal)|2| (ized power spectrum 10 log10 |S f , d0 | ∕|R|2 obtained by||
the measurement and the theoretical scattering power
spectrum for a single spherical scatterer (Fig. 2a) withdifferent diameters at every 1 µm considering the size ofa single RBC [21], the size of the RBC aggregation isestimated [10]. It is shown in the following equation:
2
��2
�
�⎤
⎡
� �
S
f
,
d
�
�
� � �⎢̂ ⎥k 0 �bQ(ka)− 10 log10𝜀(a, b) =w fk ⎢10 log10 �
⎥,
2
2
4𝜋a
�R�
k=0
⎥
⎢
⎦
⎣
N−1

(14)
( )
where w fk is the weighting function and b is the interceptof the theoretical spectrum. In the conventional and proposed methods, the nor malized power spectra2
10 log10 ||S(f , d0 )|| ∕|R|2 were obtained without and with consideration of the propagation attenuation component)|2 | ()|2| (10 log10 |AS f , d0 | ∕|Ar f , d0 | in Eq. (3), respectively. The| (| )||
weighting function w fk is calculated from the amplitude of
the scattered power PS (f , d) obtained from RBCs. Since thepower spectrum PS (f , d) of the scatterer( )changes at eachmeasurement, the weighting function w fk is calculated ateach measurement for estimating the scatterer size. Figure 2b shows the measured normalized power spectrum, thetheoretical power spectrum that minimizes ε, and the weighting function.

Basic experiments using microparticles
To verify the accuracy of the proposed method, we experimented using microparticles with known sizes. The sizes ofthe microparticles were 5 and 20 µm in diameter, and eachaqueous solution with a microparticles volume ratio of 5, 7,
and 10% was prepared in a beaker. To disperse the microspheres, polyxyethelene octylphenyl ether was used as thesurfactant. The surface of the ultrasonic probe was inserted
into the solution in a steady state. Using the Tomey Ultrasound Diagnostic System UD-8000 with a mechanical sector probe (center frequency: 40 MHz, wavelength: 38.5 µm,
focal point: 9 mm), 19 frames of RF signals were acquired
every 5 s at a sampling frequency of 240 MHz. The number()
of beams was 113 per frame. The pairs of positions d1 , d2of the window used for the attenuation calculation were set
at three different positions, (A) (8.25: 9.75 mm), (B) (8.5:
9.5 mm), and (C) (8.75: 9.25 mm), which were the same
distances from( the)depth (of 9 mm
) to cancel out the scattering
properties S f , d1 and S f , d2 in in vivo experiments. Eachwindow width was 240 µm. The propagation attenuation
components were calculated at each frame using the attenuation coefficient calculated at each frame, and the particle
sizes were estimated using both the conventional method
without correcting the propagation attenuation component
and the proposed method with the correction.

In vivo measurements
RBC aggregation is likely to occur at low shear rates [13,22, 23]. Therefore, a situation in which RBC aggregation
was likely to occur by avascularizing and reducing bloodflow was modeled in addition to without avascularization.
RF signals from blood were obtained when RBCs were
aggregated and not aggregated. The measurement target was
the dorsal vein near the skin. RF signals were acquired at asampling frequency of 240 MHz using a Tomey UD-8000

Fig. 2  Size estimation by fitting theoretical and measured scattering properties. a Theoretical properties for each scatterer size [19]. b Fitting
results for theoretical and measured properties with a weighting function

13

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ultrasound system (center frequency: 40 MHz, wavelength:38.5 µm, focal point: 9 mm). The measurement procedure
was as follows. First, the posterior wall of the vein was set
at a depth of 9 mm, and RF echoes from the lumen-intima
interface were acquired. Then, setting the center of the vascular lumen to a depth of 9 mm, we measured a total of 19
frames; 7 frames every 10 s before avascularization and 12
frames every 10 s during avascularization. The propagation
attenuation component was calculated at each frame using
the attenuation coefficient calculated at each frame, and theaggregation sizes were estimated without and with correction of the propagation attenuation components. The power
spectra were calculated for 339 RF signals obtained from
113 beams with Hanning windows of 240 µm at three different positions in the lumen, and they were averaged. The
central window was set to a depth of 9 mm, and the remaining two windows were set to a depth shifted up or down by
120 μm from the focal depth for each beam. The subjects
were two healthy males.

Journal of Medical Ultrasonics (2021) 48:3–12

Results and discussion
Basic experiments using microparticles
The attenuation coefficients were measured for three solutions; 5-µm and 20-µm microparticles were dissolved,
respectively, in two solutions, and they were mixed at aratio of 1:1 in a solution. Figure 3 shows B-mode images ofeach solution at a 5% volume ratio, power spectra, and theattenuation coefficients 𝛼m (f ) calculated with windows at
positions (A) (8.25: 9.75 mm), (B) (8.5: 9.5 mm), and (C)(8.75: 9.25 mm). As shown in Fig. 3, the attenuation coefficients 𝛼m (f ) increased as the size increased. Comparing theattenuation coefficients at different window positions withthe three solutions, similar properties were exhibited at positions (A) and (B), but the slope at position (C) was steeper
than those at positions (A) and (B). This suggests that thecalculation of the attenuation coefficient requires sufficientdistance between two windows.

Fig. 3  B-mode images and attenuation coefficients for microparticles. a B-mode image. b Power spectrum. c Attenuation coefficient 𝛼m (f ). (1)5 µm. (2) Mixed with 5 µm and 20 µm. (3) 20 µm

13Journal of Medical Ultrasonics (2021) 48:3–12

9Figure 4 shows the size estimation results. With theconventional method, the estimated size increased as thevolume ratio increased for all particle sizes. It was considered that the higher the volume ratio, the higher theattenuation caused by the scattering in the propagation
path, remarkably in the higher-frequency components. It
caused the slope of the spectrum to become gentler, andthe size was estimated to be large. With the estimation
using the proposed method, almost the same sizes were
estimated regardless of the volume ratio for 5-µm particles, and they were closer to the true size compared tothe conventional method. It was also shown that the proposed method gave almost the same sizes regardless ofthe volume ratio change even in the solution in which thetwo kinds of particles were mixed and the 20-µm particle
solution with window positions (A) and (B). For 20-µm
particles, the sizes estimated with the proposed method
were slightly smaller than 20 µm with window positions(A) and (B). When we observed a 20-µm microparticle
solution using an optical microscope, it was confirmed thatthe particle sizes were approximately ranged from 15 to
22 µm. Therefore, the particle sizes were estimated to besmaller than 20 µm with the proposed method, but it could
be within a reasonable range. The variations of the estimated sizes became large with window position (C). Thissuggests that the accuracy of the estimated attenuation
coefficient obviously affects the accuracy of the estimatedsize. With the proposed method, the attenuation coefficient
was estimated at each frame. Therefore, the variations of
the estimated sizes became larger than those yielded by
the conventional method caused by the variations of theestimated attenuation coefficients.
Figure 5 shows examples of the size estimation fittedwith the conventional method and the proposed one. With
the proposed method, the slope of the measured spectrum
was steeper than that obtained by the conventional method,
and the estimation size was smaller than that estimatedby the conventional method. It was possible to estimate
a value close to the true size with the proposed method
regardless of the volume ratio or the particle size, andit was demonstrated that the estimation accuracy of theparticle size was improved. Moreover, it was also demonstrated that the attenuation coefficients 𝛼m (f ) could beproperly estimated.

Fig. 4  Size estimation results for microparticles. a 5 µm. b Mixedwith 5 µm and 20 µm. c 20 µm. d Variation in the estimated sizesfor different volume ratios. The estimated results with the window at

position (C) (8.75: 9.25 mm) were plotted shifted left in the x direction in a–c. The results for the mixed solution were plotted at 12.5 µm
for convenience

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Journal of Medical Ultrasonics (2021) 48:3–12

Fig. 5  Fitting results of measured and theoretical scattering properties using the conventional and proposed methods. (a) 5 µm. (b) 20 µm

In vivo measurements
In blood vessels, the blood flow at the center of the bloodvessel is faster than that near the wall due to the effect oflaminar flow. Since RBC aggregation is more likely to occur
as blood flow is slower, it is necessary to set the analysis
window at a position at which the blood flow velocity is
the same when calculating the attenuation coefficients. The
measurement depth d0 , which corresponds to the center ofthe lumen, was set at 9 mm, and the attenuation coefficients�
𝛼b (f ) and 𝛼b (f ) were calculated with windows at positions(8.25: 9.75 mm), at which the estimation result was the mostaccurate in the basic experiment using microparticles. Figure 6 shows the B-mode images and the attenuation coef�ficients 𝛼b (f ) and 𝛼b (f ) of subject A before and during avascularization. The 0th–6th frames before avascularization and12th–18th frames during avascularization were averaged,
and the error bars were the standard deviations among theseseven frames. The red and blue frames in the B-mode images
indicate the window positions (8.25: 9.75 mm). From these
B-mode images, it can be confirmed that RBC aggregation occurred during avascularization, the brightness of thelumen increased, and the attenuation coefficient got larger.
The slope of frequency characteristics of attenuation coefficients became larger during avascularization in the frequency bandwidth of 27–45 MHz of the ultrasound probe
used in the measurements.
Figure 7 shows the results of RBC size estimation using
the conventional method and the proposed method for subjects A and B. The results estimated with the conventional
method and the proposed method corrected by the attenuation coefficient at each frame are indicated by red circles

13

and green triangles, respectively. The averaged attenuation
coefficients, which were obtained for the 0th–6th frames
before avascularization and the 12th–18th frames during
avascularization, as shown in Fig. 6, were also used for the
proposed method for the 0th–6th frames and 12th–18th
frames, respectively, and the results are shown in Fig. 7
with blue inverted triangles. The averaged attenuation
coefficients were not used for the 7th–11th frames, because
the attenuation coefficient varied with elapsed time fromthe beginning of the avasularization. When the attenuation
coefficient was corrected at each frame, the size variation
at each frame became large. However, when the averaged
attenuation was used for the correction, the variations
were reduced. The average estimated sizes and the standard deviations with correction using the averaged attenuation coefficients and without correction are summarizedin Table 1. Significant size differences between at rest andduring avascularization were not obtained between withand without attenuation correction in spite of using the
averaged attenuation coefficient. It might be caused by thefact that the variation of the spectra was large even though
339 spectra were averaged. In the future, we will discuss amethod to correct the propagation attenuation component
more accurately by selecting the beams at averaging of thepower spectra and using multiple points such as attenuation imaging [24].
Acquisition of reproducible data with our method
in vivo is another issue to solve, because the data dependon blood glucose status, blood flow, and so on. Moreover,
it is important to increase the sample size to investigate
the reproducibility and demonstrate the usefulness of thesize estimation method.

Journal of Medical Ultrasonics (2021) 48:3–12

11Fig. 6  B-mode images and attenuation coefficients in in vivo measurement. a B-mode image (before avascularization). b B-mode image (during�avascularization). c Attenuation coefficients 𝛼b (f ) and 𝛼b (f )Fig. 7  Size estimation results in in vivo measurements. a Subject A. b Subject B
Table 1  Size estimation results
in in vivo measurements. Values
in parentheses are the standard
deviation

At rest (0th–7th frames)

Subject A
Subject B

Avascularization (12th–18th frames)

Without correction

With correction

Without correction

With correction

7.6 (2.2)
5.6 (3.4)

6.1 (2.7)
5.4 (3.4)

25.0 (3.4)
15.7 (3.4)

28.7 (3.9)
17.1 (6.1)

13

12

Conclusion
In the present study, we tried to improve the accuracy of thesize estimation method by deriving the intravascular ultrasonic propagation attenuation and correcting the propagation
attenuation component.
When the attenuation coefficient was calculated in an
measurement using microparticles, it was confirmed thatthe attenuation coefficient increased as the particle size
and the volume ratio increased. The attenuation coefficient
could be calculated precisely when the distance between
windows was long. In the case of the conventional method,
the size estimation accuracy became worse as the volume
ratio became higher. By removing the propagation attenuation component using the proposed method, it was possible to estimate it with a nearly constant value regardlessof the change in the volume ratio, which suggested that the
proposed method could stably estimate the size regardlessof differences in hematocrit levels or the degree of RBC
aggregation. In in vivo measurement, significant differences
could not be obtained with and without the attenuation correction. This might have been caused by the large variationin the measured spectra. Going forward, we will investigate
a method to correct the propagation attenuation component
more accurately.
Acknowledgements This work was partly supported by JSPS
KAKENHI through Grant no. 19K22943.

Compliance with ethical standards
Conflict of interest The authors have no conflicts of interest concerning the presented research.
Ethical statement Informed consent to the protocol was obtained fromcontrol subjects. The study was approved by our institutional ethics
committee for human research.

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