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REGULAR PAPER

Estimation of aggregate size of red blood cell byintroducing reference power spectrum measured
for hemispherical ultrafine wire
To cite this article: Kyohei Higashiyama et al 2022 Jpn. J. Appl. Phys. 61 SG1046

View the article online for updates and enhancements.

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REGULAR PAPER

Japanese Journal of Applied Physics 61, SG1046 (2022)
https://doi.org/10.35848/1347-4065/ac4683

Estimation of aggregate size of red blood cell by introducing reference power
spectrum measured for hemispherical ultrafine wire
Kyohei Higashiyama1, Shohei Mori2, Mototaka Arakawa1,2*, Satoshi Yashiro3, Yasushi Ishigaki3, and Hiroshi Kanai1,2
1Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan
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, Japan2*

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

Received November 2, 2021; revised December 16, 2021; accepted December 26, 2021; published online May 30, 2022
Noninvasive measurement of the degree of red blood cell (RBC) aggregation is useful for evaluating blood properties. In the present paper, we
proposed a method to estimate the size of RBC aggregates without using the power spectrum of the posterior wall by introducing a reference
scattering spectrum. The reference power spectra were calculated using the power spectrum measured for an ultrafine wire with a hemisphericaltip. They were applied to the size estimation of microparticles simulating RBC aggregates. The estimated sizes were close to the true values, whichshows that the calculated reference power spectra were suitable for accurate size estimation. The proposed method was also applied to in vivo
measurements, and the estimated sizes between at rest and in RBCs aggregated by avascularization were successfully differentiated. This
demonstrates that the proposed method will be useful for estimating the size of RBC aggregates. © 2022 The Japan Society of Applied Physics

1. Introduction

Red blood cells (RBCs) in blood adhere to each other at alow shear rate.1–3) This reversible phenomenon is called RBC
aggregation. RBC aggregation in plasma is enhanced byfactors such as increased levels of macromolecular compounds (ﬁbrinogen and macroglobulin) in the blood.
Excessive RBC aggregation is frequently observed in diseases such as type II diabetes, deep vein thrombosis, andsepsis,4–6) and is thought to interfere with vasomotor tone,
leading to the progression of high blood pressure. It may
negatively affect the microcirculation and nutrient supply.7,8)
The increase in RBC aggregation is known to increase theblood viscosity in large vessels, such as veins in the lower
extremities with low shear force,6,9) and it is an indicatorhighly related to blood properties. Therefore, the evaluationof RBC aggregation is clinically meaningful for the evaluation of blood properties as well as the screening of these
diseases.
Increased RBC aggregation can be observed as theincreased brightness of the vessel lumen (smoke-like echo)
on ultrasound B-mode images.10,11) Although the evaluationof blood properties based on the smoke-like echo is useful, it
is qualitative.12,13)
There are several studies on the quantitative evaluation of
RBC aggregation using ultrasound. Shung et al. observedchanges in the brightness of porcine blood echoes during a
cardiac cycle,14,15) and Patat et al. observed the changes inthe sound velocity and the scatterer size during blood
coagulation using human whole blood in vitro.16,17) All ofthese evaluation methods were applied to the blood drawn by
blood sampling; therefore, they were invasive.
The evaluation of ultrasound backscattering characteristics
is a quantitative method for tissue characterization. By
estimating the backscatter coefﬁcient and the attenuation
coefﬁcient of the tissue based on the frequency spectrum of
the radiofrequency (RF) signal obtained from the object, thestructural parameters, such as, the shape, size, and concentration can be estimated. This method has been applied forthe analysis and classiﬁcation of various tissues, such as, theliver, skin, lymph nodes, and blood.18–27)

Cloutier et al. calculated the backscattering coefﬁcientfrom the RF signal obtained from the vascular lumen
and estimated the attenuation coefﬁcient of tissues and theparameters indicating the structure of the RBC
aggregates,24–26) and showed the possibility of monitoring
the systemic inﬂammatory state by in vivo measurements.27)
However, few studies using these methods have involved
human subjects, and diagnosis using this method has notbeen clinically established.
We have studied a noninvasive and quantitative method
for measuring blood properties.28–37) Saito et al. assumed that
RBCs aggregate as a single-sphere scatterer and estimated thesize from the scattering characteristics extracted by normalizing the power spectrum measured from the vessel lumen
with that from the rear wall using a focused ultrasoundtransducer.28–32) We also examined the relationship between
RBC aggregation using ultrasound and blood glucose level.
Sakaki et al. compared the blood glucose levels with theparameters determined from changes in the scattering power
spectra of the echoes from the vascular lumen before andafter avascularization.33,34) Fukase et al. studied the relationship between the blood glucose levels and the brightness
values of the B-mode image.35) However, there are still
problems, such as the low correlation between these parameters and the blood glucose levels and the lack of
reproducibility of the results because of the variation in thedata among the measurements. The development of a moreaccurate method for evaluating the degree of RBC aggregation would solve these problems.
In our estimation method of the RBC aggregate size, we
regarded the rear wall of the vessel as the reﬂector, and thereﬂection property at the rear wall was assumed to be
independent of frequency. However, because high-frequency
ultrasound with a center frequency of approximately 40 MHz
was used, the reﬂection characteristics of the rear wall might
have frequency dependence owing to the surface roughness
and the slope of the vessel wall to the probe surface. This
causes errors in the size estimation results.
Moreover, Fukase et al. suggested that the effect ofelevational misalignment of vessels in the long-axis measurement on the evaluation of the degree of RBC aggregation

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could be reduced by short-axis measurement.36) However, inthe short-axis measurement of the vessel, few beams can beused as the signal of the rear wall, making it difﬁcult toremove the dips that appear on the averaged power spectrum.
Therefore, robust size estimation using short-axis measurements could be difﬁcult.
To directly estimate the size of the RBC aggregates using
only the scattering power spectrum obtained from thevascular lumen, we measured the power spectra for the threewires with a hemispherical edge assumed to be a singlesphere scatterer to calculate the reference scattering power
spectra. Subsequently, the ratios of the power spectra
measured for the two wires with different diameters were
calculated using three combinations. The ratios were compared with those of the theoretical scattering power spectra
corresponding to the diameters of the wires to evaluate theaccuracy of the reference power spectra.37) In the present
paper, we estimated the size of the microparticles withdifferent diameters to evaluate the accuracy of the proposed
size estimation method using the reference scattering power
spectrum. Moreover, we investigated the clinical usefulnessof our method by estimating the size of RBC aggregates inthe dorsal hand vein.
2. Principle and methods
2.1. Calculation of the reference power spectra

In the present paper, the RBC aggregate was assumed to be asingle-sphere scatterer with numerous point sources on thesurface. The theoretical power spectrum obtained by irradiating a plane wave is expressed as
Q (ka )=
4pa 2¥

2n + 1

å (ka) sin2 [d¢n (ka)] ,
2

(1 )

n=0

where Q (ka ) is the scattering cross section, k is thewavenumber, a is the radius of the scatterer, n is the numberof point sources on the surface of the scatterer, and d¢n (ka ) is
the derivative of the phase difference between the incident
and scattered waves.38) Figure 1(a) shows the power spectra
calculated using Eq. (1) for scatterer sizes of 2–60 mm. Here,the biological sound speed (c = 1540 m s-1) was assumed,

and the wavenumber k was converted to frequency f using
the relation f = ck /2p. As shown in Fig. 1(a), the slope of
the power spectrum decreased as the scatter size increased.
The size of the RBC aggregate was estimated using theinclination differences in the frequency dependence among
the scatterer sizes.
In the present paper, the scattering power spectrum
Ps ( f , d ) was obtained by measuring the vascular lumen at a
depth d. Ps ( f , d ) includes not only the scattering property
S ( f ) but also the frequency dependence of the applied signal
X ( f ), transmission and reception properties of the ultrasonictransducer G ( f ), sound pressure property of the ultrasoundprobe at depth d, H ( f , d ), and attenuation property A ( f , d ).
Therefore, the scattering power spectrum Ps ( f , d ) from thevascular lumen at depth d is given by:Ps ( f , d ) = ∣ S ( f ) X ( f ) G ( f ) H ( f , d ) A ( f , d )∣2 .

(2 )Thus, the reference power spectrum PRD ( f , d ) for thecomparison with Ps ( f , d ) is given by
P RD ( f , d ) = ∣ SD ( f ) X ( f ) G ( f ) H ( f , d ) A ( f , d )∣2 ,(3 )where SD ( f ) is the theoretical scattering property of a single
sphere with diameter of D. In the present paper, the reference
power spectrum PRD ( f , d ) was calculated by measuring theultraﬁne wire with a hemispherical tip. Let us deﬁne thepower spectrum Pf ( f , d ) obtained from the ultraﬁne wire at
depth d in water as
Pf ( f , d ) = ∣ Sf ( f ) X ( f ) G ( f ) H ( f , d ) Aw ( f , d )∣2 ,(4 )where Aw ( f , d ) is the attenuation property of the water. The
reference scattering power spectrum PRD ( f , d ) with anarbitrary diameter D is obtained by the product of Pf ( f , d )and the ratio ∣ SD ( f )∣2 /∣ Sf ( f )∣2 of the theoretical power to thepower of the wire, as follows:
P RD ( f , d ) = Pf ( f , d ) ´SD ( f )Sf ( f )

2

.

(5 )

2.2. Estimation of the size of RBC aggregates

Wires in water were used as the targets to obtain the reference
power spectrum. Ultrasound propagates in the skin and blood

(b)

(a)

Fig. 1. (Color online) (a) Theoretical scattering power spectra 10 log10 {Q (ka ) /4pa 2} and (b) the schematic diagram of the in vivo measurement.

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after propagation in the water in the membrane attached tothe probe in vivo. Therefore, it is inappropriate to directly ﬁt
the measured power spectrum to the calculated reference
scattering power spectra because there is an attenuation
characteristic difference owing to the different propagation
paths of the two measurements. The correction componentCs ( f , d ) which shows the difference in propagation attenuation characteristics between in vivo and wire measurements,
was calculated using the propagation path of the skin d c, thatof the blood db, and the attenuation coefﬁcient of the skinac ( f ), that of the blood a b ( f ), and that of the water a w( f ) as
follows:

Pr ( f , d1)
Pr ( f , d2 )∣ R A ( f , d1) H ( f , d1) G ( f ) X ( f )∣2= 10 log10 0 w∣ R 0 Aw ( f , d2 ) H ( f , d2 ) G ( f ) X ( f )∣2∣ H ( f , d1)∣2∣ Aw ( f , d1)∣2= 10 log10
+
10
log
,
10
∣ H ( f , d2 )∣2∣ Aw ( f , d2 )∣2

10 log10

where, R0 is the reﬂectance property of the reﬂector. By
solving Eq. (10) for 10 log10 ∣ H ( f , d1 )∣2 /∣ H ( f , d 2 )∣2 , thedifference in the sound pressure properties can be obtained asfollows:

Cs ( f , d ) = 2d c a c ( f ) + 2db a b ( f ) - 2 (d c + db ) aw ( f ).

∣ H ( f , d1)∣2
P ( f , d1)= 10 log10 r
2∣ H ( f , d2 )∣Pr ( f , d2 )2∣ A ( f , d1)∣
- 10 log10 w.
∣ Aw ( f , d2 )∣2

10 log10(6 )The ﬁrst and second terms on the right-hand side of Eq. (6)shows the propagation attenuation in the in vivo measurement, and the third term shows that in the measurement of thewire.
The attenuation coefﬁcient of the skin ac ( f ) was calculated by correcting the difference in the sound pressure
properties for the difference in the power spectra measured at
the different depths d1 and d 2 in the target.32) The ratio of themeasured power spectra Pc ( f , d1) and Pc ( f , d 2 ) at different
depths d1 and d 2, respectively, by setting the focal point at a
depth of d 0 = d w + d c /2 in Fig. 1(b) corresponds to thesum of the difference in the attenuation properties∣ Ac ( f , d1 )∣2 /∣ Ac ( f , d 2 )∣2 and difference in the sound pressure properties ∣ H ( f , d1 )∣2 /∣ H ( f , d 2 )∣2 are as follows:
Pc ( f , d1 )Pc ( f , d2 )∣ Sc ( f ) A w ( f , d w ) A c ( f , d1 - d w ) H ( f , d1 ) G ( f ) X ( f )∣2= 10 log10∣ Sc ( f ) A w ( f , d w ) A c ( f , d2 - d w ) H ( f , d2 ) G ( f ) X ( f )∣2∣ A c ( f , d1 - d w )∣2∣ H ( f , d1 )∣2,+ 10 log10= 10 log102∣ A c ( f , d2 - d w )∣∣ H ( f , d2 )∣2

10 log10

(7 )

(10)

(11)

The difference in the attenuation properties of water∣ Aw ( f , d1 )∣2 /∣ Aw ( f , d 2 )∣2 can be calculated from Eq. (8)using the attenuation coefﬁcient of water aw ( f ).39) The
attenuation coefﬁcient ac ( f ) can be calculated by substituting ∣ H ( f , d1 )∣2 /∣ H ( f , d 2 )∣2 in Eq. (9). In addition, theattenuation coefﬁcient of blood a b ( f ) is calculated using thesame procedure by setting the focal point at the center of thevascular lumen. That is, Ps ( f , d1) and Ps ( f , d 2 ) are calculated
by changing the analysis window positions for the measured
signal to obtain the power spectrum measured from thevascular lumen Ps ( f , d ).
After correcting the power spectrum measured from thevascular lumen Ps ( f , d ) by multiplying the calculated correction term Cs ( f , d ), the corrected power spectrum Ps¢ ( f , d )and the reference scattering power spectra were ﬁtted using
the weighted least-squares method, as shown in Eq. (12).
Thereafter, the size of the RBC aggregate was estimated byminimizing the following error DPD.
N-1

DPD = å w (fk )[10 log10 Ps¢ ( fk , d )where, Sc ( f ) is the scattering characteristics of the skin.
Subsequently, the attenuation property ∣ A ( f , d )∣ is expressedusing the attenuation coefﬁcient a ( f ) as:

k= 0- 10 log10 P RD ( fk , d ) + b ]2 ,(12)a( f )∣ A ( f , d )∣ = e-2d ´ 8.686 ,(8 )where, e is the base of the natural logarithm, and 10 log10 e 2= 8.686. From Eqs. (7) and (8), the attenuation coefﬁcientac ( f ) can be expressed as follows:ac ( f ) =1⎧10 log Pc ( f , d1)
10
2 (d2 - d1) ⎨Pc ( f , d2)⎩- 10 log10∣ H ( f , d1)∣2 ⎫[dB mm-1].
∣ H ( f , d2 )∣2 ⎬⎭(9 )The difference in the sound pressure properties is acquired inadvance by the measurements for a reﬂector set at different
depths in water. The ratio of the power spectra Pr ( f , d1) andPr ( f , d 2 ) for the reﬂector measured at different depths d1 andd 2, respectively, corresponds to the sum of the difference insound pressure properties ∣ H ( f , d1 )∣2 /∣ H ( f , d 2 )∣2 andthe difference in the attenuation properties of water∣ Aw ( f , d1 )∣2 /∣ Aw ( f , d 2 )∣2 as follows:

where b is the intercept of the theoretical spectrum and w ( fk )is the weighting function deﬁned to use a reliable frequency
range for the ﬁtting and is calculated by dividing the power
spectrum in water without the object from the obtained
scattered power spectrum Ps ( f , d ).
2.3. Experiment2.3.1. Measurement for the ultrafine wires. An ultraﬁnewire with a hemispherical tip was set parallel to the beam
direction (z-axis direction) of the ultrasonic probe for theultrasound measurement, as shown in Fig. 2(a), where d w is
the propagation path length of water. Figure 2(b) shows amicrograph of the wire (diameter f = 40 mm ). An ultrasoundsystem (Tomey UD-8000) was used. The sampling frequency
was 240 MHz. A mechanical scanning linear probe with anoperating center frequency of 30 MHz (frequency range: 19–
40 MHz) was used. The focal length of the probe, this iscomposed of a concave transducer and a mechanical scanner,
was 8.75 mm, and the distance between the ultrasonictransducer and the tip of the wire d 0 was set to 8.75 mm.

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K. Higashiyama et al.

(a)

(b)

(c)

Fig. 2. (Color online) (a) Schematic diagram of the wire measurement, (b) micrograph of a wire (f = 40 mm ), and (c) schematic diagram of the phantom
measurement.

Ultraﬁne wires with diameters {f} of 20, 30, and 40 μm wereused. To accurately align the measurement position of the tipof the wire, the mechanical scanning of the ultrasound probe
was stopped and it was manually moved with a 2 μm step ineach of the x-axis and y-axis directions to obtain the largest
amplitude of the signal from the tip of the wire. The power
spectrum Pf ( f , d 0 ) was calculated by windowing the RF
signal with a rectangular window with a width of 0.2 μs.
In addition, when the accurate scattering property S ( f ) is
included in the calculated power spectrum Pf ( f , d 0 ), the ratioof the scattering power spectra obtained from single-spherescatterers with different diameters f1 and f2 agree with thatof the theoretical powers with diameters f1 and f2 , as
Pf1 ( f , d )=P ( f , d)f2

Sf1 ( f ) G ( f ) X ( f ) H ( f , d ) A ( f , d ) 2
Sf 2 ( f ) G ( f ) X ( f ) H ( f , d ) A ( f , d )=Sf1 ( f ) 2
Sf 2 ( f )

.

(13)

This relationship was used to evaluate the accuracy of thescattering characteristics included in the power spectrum
Pf ( f , d 0 ) measured for the wire.
2.3.2. Phantom experiment. To evaluate the accuracy ofthe proposed size estimation method, the sizes of the
microparticles simulating RBC aggregates were estimatedusing reference power spectra. Based on Eq. (5), thereference power spectra PRD ( f , d 0 ) were calculated with a
1 μm step in the range of D = 2–60 μm using the power
spectrum P20 ( f , d 0 ) obtained from the wire with a diameterof 20 μm. Blood-simulating phantoms were prepared bysuspending microparticles with diameters of 5 and 20 μm in
water. Accurate measurements are difﬁcult for microparticles
with high volume ratios because of the large attenuation
owing to the large difference in acoustic impedances between
the particles and water. Thus, the volume ratio of the particles
was set to 1%.
The experimental system for the B-mode is shown in
Fig. 2(c). The number of beams was 113, and 20 frames wereacquired. The scattering power spectrum was calculated bywindowing the acquired RF signal with a Hanning windowof width 0.15 μs centered at a depth of d 0 = 8.75 mm. The
power spectrum for the size estimation, Pm ( f , d 0 ), wascalculated by averaging the scattering power spectra with
113 beams. The term to compensate for the difference in theattenuation properties between the wire measurement andphantom measurement, Cm ( f , d ), is given by:
Cm ( f , d ) = 2d m {a m ( f ) - aw ( f )},(14)

where d m is the propagation path length of the bloodsimulating phantom, and am ( f ) is the attenuation coefﬁcientof the phantom. am ( f )was calculated from the power spectraof phantom calculated as the depths of d1 = 8.2 mm andd 2 = 9.0 mm by correcting the sound pressure characteristics
difference.32) The literature value was used as the attenuation
coefﬁcient of water aw ( f ).39) The corrected power spectrumPm¢ ( f , d 0 ) was obtained by multiplying the correction termCm ( f , d ) to Pm ( f , d 0 ) for each frame, and the size of the
microparticles was estimated by ﬁtting the corrected power
spectrum Pm¢ ( f , d 0 ) with the reference scattering power
spectra PRD ( f , d 0 ).
2.3.3. In vivo measurement. The size of the RBC
aggregate was estimated by in vivo measurements for ahealthy subject in their 20 s. First, to calculate the attenuation
coefﬁcient of the skin, ac ( f ), the RF signal was measured
from the skin by long-axis measurement by setting the focal
point at a depth of d 0 = d w + d c /2. The power spectra were
calculated by windowing the RF signal with the Hanningwindow at the depths of d1 = 8.2 mm and d 2 = 9.0 mm, andthe attenuation coefﬁcient of the skin, a c( f ), was determined. Next, the RF signal was obtained from the vascularlumen using ultrasonic short-axis measurements. The focal
point was set as the center of the lumen of the dorsal handvein, as shown in Fig. 3(a). RBC aggregation is more likely
to occur under low-shear-rate conditions. Therefore, in
addition to the measurements at rest, the RF signals were
measured under the condition of avascularization using
crucible scissors.35) The blood ﬂow was stopped by pressing
two points on the ﬁngertip side and the heart side of the vein,
as shown in Fig. 3(b), to prevent the backﬂow of the blood.
Five frames were obtained every 10 s for 0–190 s, and theblood ﬂow was stopped from 60 to 190 s. Fifteen beams ( 7beams for the beam passing through the center of the vascularlumen) were used in each frame. The power spectra
calculated by windowing the signals with a Hanning window

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K. Higashiyama et al.

(b)

(a)

Fig. 3. (Color online) (a) State of in vivo measurement and (b) state of avascularization.

with a width of 0.15 μs at the focal point of the ultrasoundprobe were averaged with 15 beams for 5 frames to obtain the
power spectrum Ps ( f , d 0 ) at each time.
The attenuation measurements for the skin, d1 and d 2, were
set to calculate the power spectra from the blood, and theattenuation coefﬁcient a b( f ) of the blood at each time point
was calculated. The correction terms Cs ( f , d 0 ) calculatedusing ac ( f ) and a b ( f ) in Eq. (6) was multiplied by thepower spectrum Ps ( f , d 0 ), and the size of the RBC aggregate
was determined by ﬁtting the corrected power spectrum andthe reference scattering power spectra. Because the bloodvessel moves signiﬁcantly immediately after avascularizationand the aggregation state is not stable owing to the inﬂuenceof the shear rate immediately before the avascularization,27)
the estimated sizes at rest (0–60 s) and that at the latter 7
frames (130–190 s) during avascularization were compared.
Moreover, to evaluate the usefulness of the proposed
method, the size of the RBC aggregates was estimated using
the conventional method.32) The scattering characteristics
were obtained by normalizing the power spectrum of thevascular lumen Ps ( f , d 0 ) with that of the posterior wall. The
RBC aggregate sizes were estimated by ﬁtting the normalized
power spectrum to the theoretical power spectrum.
Afterwards, the estimated sizes were compared with thoseestimated using the proposed method.
3. Results and discussion
3.1. Measurement for the wire

Figure 4(a) shows the power spectra Pf ( f , d 0 ) measured foreach of the hemispherical ultraﬁne wires with different
diameters {f}. The ﬁgure shows that the power increased
with a larger diameter. Figure 4(b) shows the ratios of thepower spectra Pf ( f , d 0 ) obtained from the wires withdifferent diameters {f} and the ratios of the theoreticalscattering powers ∣ Sf ( f )∣2 for the corresponding diametersof the wires. In Figs. 4(b-1), 4(b-2), and 4(b-3), the averages

and the standard deviations of the differences {e ( f )} between
them were calculated in the 6 dB-band asPf ( f , d 0 )e ( f ) = 10 log10 P 1 ( f , d ) - 10 log10
f2

0

Sf1 ( f ) 2
Sf 2 ( f )

.

(15)

The averaged differences (the standard deviations) were 1.3(0.51), 5.6 (0.38), and 7.5 (0.76) dB for Figs. 4(b-1), 4(b-2),
and 4(b-3), respectively. The standard deviations were lessthan 1 dB in all cases, although the average differences wererelatively large for Figs. 4(b-2) and 3(b-3). Thus, the power
ratio of the measured power spectra for the wires and thetheoretical scattering power ratio showed similar frequency
characteristics.
The frequency characteristics of Figs. 4(b-2) and 4(b-3)
were similar to those of the theoretical power ratio, but the
averages of the differences {e ( f )} were larger than those in
Fig. 4(b-1). This is caused by the effect of the sound pressure
distribution of the transmitted wave. In the present paper, thetransmitted wave was assumed to be a plane wave, although
the focused wave was transmitted. Thus, the sound pressure
is distributed in the lateral direction near the focus.
Figure 4(c) shows the measured amplitude distribution of
the ultrasound probe for a wire with a diameter of 30 μm bymoving the ultrasound probe in 2 μm steps in the direction of
the x-axis in Fig. 2(a). This shows that the sound ﬁeld
distribution became ﬂatter as it got away from the focal point
and approached the characteristics of a plane wave.
Figure 4(d) shows the averaged differences between the
power ratio of the measured power spectra for the wire in thecase of d 0 = 8.75 and 9.0 mm and the theoretical scattering
power ratio. The average differences at d 0 = 9.0 mm became
smaller compared to those at d 0 = 8.75 mm. Thus, the soundpressure distribution became smaller at points farther fromthe focal point. Because the measurement target was spherical, the phase of the scattered wave differed at each lateralposition. The components having phases that cancel theSG1046-5© 2022 The Japan Society of Applied Physics

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K. Higashiyama et al.

Fig. 4. (Color online) (a) The power spectra for the wires, (b) the ratio of the power spectra {Pfi ( f , d 0 )} from the wires with different diameters {fi} andtheoretical power ratio corresponding to the diameters of the wires, (b-1) f1 = 30 m m, f2 = 20 m m, (b-2) f1 = 40 m m, f2 = 30 m m, (b-3) f1 = 40 m m,
f2 = 20 m m, (c) the results of the sound ﬁeld measurements, and (d) the average of the differences e ( f ) due to change in d 0.

(a)

(b)

Fig. 5. B-mode images of the blood-simulating phantoms. (a) 5 μm and (b) 20 μm.

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backscattered power might decrease owing to the soundpressure distribution. This effect increases as the diameter ofthe wire increases, which increases the power difference
between wires with different diameters. Consequently, thecalculated power ratios of the wires may increase.
In the actual estimation of the RBC aggregate size, thefrequency dependences between the measured power spectrum and the calculated reference scattering power spectra are
ﬁtted by changing the offset to minimize the difference,
considering the difference between the ultrasonic reﬂectivity
for water and wire and that for plasma and RBCs. Therefore,
the measured spectrum Pf ( f , d 0 ) for the wire is suitable forcalculating the reference scattering power spectra because thepower ratio measured for the wires showed similar frequency
characteristics to that of the theoretical power spectra.
3.2. Phantom experiment
B-mode images of the blood-simulating phantom are shown in
Fig. 5. This shows that the image became brighter as theparticle size increased. Figure 6(a) shows the averaged power
spectra {Pm ( f , d 0 )} among the 20 frames with standard
deviations. Figure 6(b) shows the averages and standard
deviations of the calculated attenuation coefﬁcients a m ( f ) of
the blood-simulating phantoms over 20 frames. It shows thatthe calculated attenuation coefﬁcient am ( f ) was close to linear
in the 6 dB bandwidth from 19 to 40 MHz, and the attenuation
coefﬁcient am ( f ) increased as the particle size increased. A 6
dB bandwidth of 19–40 MHz was determined for the reﬂection
spectrum acquired for the reﬂector in water. Because thebackscattered power increased as the particle size increased, as
shown in Fig. 5, it is a reasonable trend that the propagation
attenuation also increased with the larger particle size.

The correction term Cm ( f , d 0 ) is calculated using Eq. (14),and the size of the particle was estimated by ﬁtting thecorrected power spectrum Pm¢ ( f , d 0 ) with the reference
power spectra PRD ( f , d 0 ). The estimated sizes are presented
in Table I. This shows that the estimated sizes are close to
the true sizes. The difference in the estimated sizes of theparticles with different sizes was also conﬁrmed. Figures 6(c)and 6(d) show the ﬁtting results of the corrected power
spectrum and the reference power spectrum, which corresponded to the estimated sizes of 5 μm and 20 μm particles,
respectively. The root means squared errors (RMSEs) of theﬁtting were 0.7 dB and 0.3 dB for the particle diameters of
5 μm and 20 μm, respectively. This shows that the corrected
power spectrum Pm¢ ( f , d 0 ) was well ﬁtted with the reference
power spectrum. These results show that the reference
scattering power spectra are useful for the accurate size
estimation of scatterers.
3.3. In vivo measurement
The size of the RBC aggregates was estimated using in vivo
measurements. Figure 7(a) shows the averaged values andstandard deviations of the attenuation coefﬁcient of the skina c( f ) for eight frames, which is similar to the frequency
characteristics in the literature.40)
Next, RF signals were acquired from the vascular lumen
by short-axis measurements. Figures 7(b-1) and 7(b-2) show
the ultrasonic B-mode images of the vascular lumen at rest
and with RBCs aggregated by avascularization, respectively.
Figure 8(a) shows the averages and standard deviations of
the power spectra Ps ( f , d 0 ) averaged over seven frames atrest and during avascularization. The attenuation coefﬁcienta b ( f ) of the blood was also calculated for each frame, andFig. 6. (Color online) (a) The power spectra measured from the blood-simulating phantom, (b) the attenuation coefﬁcient of the phantom, (c) the ﬁtting result(5 μm), and (d) the ﬁtting result (20 μm).

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Jpn. J. Appl. Phys. 61, SG1046 (2022)
Table I.

K. Higashiyama et al.

Estimated sizes of the microparticles.

Micro particles

5 μm

20 μm

Average [μm]Standard deviation [μm]

8.3
3.6

19.3
2.2

the averages and standard deviations among frames at restand during avascularization are shown in Fig. 8(b). The
attenuation coefﬁcient at rest was 2.2 dB mm−1 at 30 MHz,and that of the sampled blood was 1.2 dB mm−1 at 30 MHz
in the literature.41) It shows that the calculated a b( f ) was
close to that of the literature. Moreover, the correction termCs ( f , d 0 ) is calculated using Eq. (6), the power spectrum
Ps ( f , d 0 ) was corrected, and the size of the RBC aggregates
was estimated by ﬁtting the corrected power spectrumPs¢ ( f , d 0 ) to the reference power spectra PRD ( f , d 0 ).
Table II shows the averages and standard deviations of theestimated sizes of RBCs at rest and during avascularization.
In healthy subjects, RBCs do not aggregate without avascularization. The diameter of a single RBC was approximately
6–8 μm.42,43) In the proposed method, the average estimatedsize at rest was 8.1 μm, which is reasonable. The average
estimated size during the avascularization was 15.2 μm,
which corresponds to the increase in size due to RBC
aggregation. Figures 8(c) and 8(d) show the ﬁtting resultsof the corrected power spectrum Ps¢ ( f , d 0 ) and the reference
power spectrum at rest and during avascularization, respectively. The RMSEs of the ﬁtting in Figs. 8(c) and 8(d) were

0.7 dB and 0.2 dB, respectively, which shows that thecorrected power spectrum Ps¢ ( f , d 0 ) was well ﬁtted withthe reference power spectrum. The average of the RMSEsof the ﬁtting among frames are shown in Table III. Thisshows that the ﬁtting error in the proposed method is smaller
than that in the conventional method.
In the conventional method, the average of the estimatedsize at rest was 25.1 μm, which was much larger than the
diameter of a single RBC, and the normalized power
spectrum did not ﬁt well with the theoretical power spectrum,
as shown in Fig. 9(a). The power spectra of the posterior wallmight be frequency dependent due to the slope and surface
shape of the posterior wall. In fact, the power spectra of theposterior wall that were used for the size estimation variedamong the beams, as shown in Fig. 9(b). This probably
affected the accuracy of the size estimation using theconventional method. Moreover, in this study, the shortaxis scan was used for the measurement to reduce the effectof the elevational misalignment of vessels in the long-axis
measurement.36) In this measurement, the number of beams
that can be used as the signals of the posterior wall is small,and the effect of the dip caused by the unwanted signals
included in the analysis range of the posterior wall might not
be removed. This might increase the ﬁtting error of theconventional method.
In the proposed method, the corrected power spectrumPs¢ ( f , d 0 ) ﬁtted well with the reference power spectrum, eventhough the scattered waves from RBCs interfered with eachother. The effect of interference might be reduced by

Fig. 7. (Color online) (a) The estimated attenuation coefﬁcient of the skin, (b-1) B-mode image at rest, and (b-2) B-mode image during avascularization.

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Jpn. J. Appl. Phys. 61, SG1046 (2022)

K. Higashiyama et al.

Fig. 8. (Color online) (a) The power spectra measured for the vascular lumen, (b) the attenuation coefﬁcient of blood, (c) the ﬁtting result at rest, and (d) theﬁtting result during avascularization.
Table II.

Estimated sizes of RBC aggregates (unit: μm).
At rest

Proposed
Conventional

AverageSD

Average

SD

8.1
25.1

2.9
7.2

15.2
59

2.8
0

Table III.

Proposed
Conventional

During avascularization

RMSEs of ﬁtting (unit: dB).
At restDuring avascularization

0.7
1.5

0.3
0.8

averaging the scattering power spectra. These results showthat the proposed method will be useful for the accurate
evaluation of the degree of RBC aggregation.
4. Conclusions

In the present paper, a method for estimating the size of RBC
aggregates without using the power spectrum of the rear wall
was proposed by introducing a reference scattering power
spectrum calculated by the power spectrum measured for
ultraﬁne wires with a hemispherical tip. The size of the
microparticles simulating the RBC aggregates was estimatedusing the reference scattering power spectra calculated fromthe power spectrum measured for the ultraﬁne wire. As a

(a)

(b)

Fig. 9. (Color online) (a) Fitting results by the conventional method, and (b) power spectra of posterior wall which were used for the size estimation by theconventional method.

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Jpn. J. Appl. Phys. 61, SG1046 (2022)

K. Higashiyama et al.

result, the estimated size was close to the true value, and it
shows that the reference power spectra are useful for accurate
size estimation of the scatterer sizes. Moreover, the proposed
method was applied to in vivo measurements. The estimatedsize at rest was similar to the size of a single RBC andincreased when the RBCs were aggregated by avascularization.
Wires with a hemispherical tip were used for the measurements, but the theoretical model assumed the object to be asphere. It is necessary to clarify the effect of the deviation of
the model on the size estimation. However, the results of thispaper show that the proposed method will be useful for
accurate size estimation of RBC aggregates.
Acknowledgments

This work was partially supported by JSPS KAKENHI
19K22943.

R. Fåhraeus, Physiol. Rev. 9, 241 (1929).
S. Chien and K. Jan, Microvasc. Res. 5, 155 (1973).
S. Chien and L. A. Sung, Clin. Hemorheol. Microcirc. 7, 71 (1987).
O. K. Baskurt, A. Temiz, and H. J. Meiselman, J. Lab. Clin. Med. 130, 183(1997).
5) G. Cloutier, A. Zimmer, F. T. Yu, and J. L. Chiasson, Diabetes Care 31,
1400 (2008).
6) F. T. Yu, J. K. Armstrong, J. Tripette, H. J. Meiselman, and G. Cloutier, J.
Thromb. Haemost. 9, 481 (2011).
7) O. K. Baskurt, A. Herbert, and J. Meiselman, Microcirculation 15, 585(2008).
8) J. J. Bishop, P. R. Nance, A. S. Popel, M. Intaglietta, and P. C. Johnson, Am.
J. Physiol. Heart Circ. Physiol. 280, H222 (2001).
9) J. W. Weisel and R. I. Litvinov, J. Thromb. Haemost. 17, 271 (2018).
10) D. G. Paeng, K. H. Nam, and K. K. Shung, Ultrasound Med. Biol. 36, 1118
(2010).
11) D. G. Paeng, K. H. Nam, M. J. Choi, and K. K. Shung, IEEE Trans.
Ultrason. Ferroelectr. Freq. Control 56, 880 (2009).
12) S. Beppu, Y. Nimura, H. Sakakibara, S. Nagata, Y. D. Park, and S. Izumi, J.
Am. Coll. Cardiol. 6, 744 (1985).
13) S. Turhan, O. U. Ozcan, and C. Erol, Cor et Vasa 55, 176 (2013).
14) D. G. Paeng, R. Y. Chiao, and K. K. Shung, Ultrasound Med. Biol. 30, 45(2003).
15) D. G. Paeng, R. Y. Chiao, and K. K. Shung, Ultrasound Med. Biol. 30, 815(2004).
16) R. L. Callé, F. Ossant, Y. Gruel, P. Lermusiaux, and F. Patat, UltrasoundMed. Biol. 34, 252 (2008).
17) R. Callé, C. Plag, F. Patat, and F. Ossant, J. Acoust. Soc. Am. 125, 530(2009).
1)
2)
3)
4)

18) D. Nicholas, Ultrasound Med. Biol. 8, 17 (1982).
19) T. Oguri, M. Omura, W. Saito, K. Yoshida, and T. Yamaguchi, Jpn. J. Appl.
Phys. 60, SDDE24 (2021).
20) T. Oguri, K. Tamura, K. Yoshida, J. Mamou, H. Hasegawa, H. Maruyama,
H. Hachiya, and T. Yamaguchi, Jpn. J. Appl. Phys. 54, 07HF14 (2015).
21) T. M. Bui, A. Coron, J. Mamou, E. Saegusa-Beecroft, T. Yamaguchi,
E. Yanagihara, J. Machi, S. L. Bridal, and E. J. Feleppa., IEEE Trans.
Biomed. Eng. 64, 1579 (2017).
22) M. Omura, K. Yoshida, S. Akita, and T. Yamaguchi, Jpn. J. Appl. Phys. 59,
SKKE15 (2020).
23) M. Omura, K. Yoshida, S. Akita, and T. Yamaguchi, J. Med. Ultrason. 47,
25 (2020).
24) E. Franceschini, F. T. H. Yu, and G. Cloutier, J. Acoust. Soc. Am. 123,
EL85 (2008).
25) E. Franceschini, F. T. H. Yu, F. Destrempes, and G. Cloutier, J. Acoust. Soc.
Am. 127, 1104 (2010).
26) R. K. Saha, E. Franceschini, and G. Cloutier, J. Acoust. Soc. Am. 129, 2269
(2011).
27) B. Chayer, L. Allard, Z. Qin, J. Garcia-Duitama, L. Roger, F. Destrempes, J.
F. Cailhier, A. Denault, and G. Cloutier, Clin. Hemorheol. Microcirc. 74,
109 (2020).
28) N. Saitoh, H. Hasegawa, and H. Kanai, Jpn. J. Appl. Phys. 48, 07GJ08(2009).
29) T. Fukushima, H. Hasegawa, and H. Kanai, Jpn. J. Appl. Phys. 50, 07HF02(2011).
30) Y. Kurokawa, H. Taki, S. Yashiro, K. Nagasawa, Y. Ishigaki, and H. Kanai,
Jpn. J. Appl. Phys. 55, 07KF12 (2016).
31) M. Arakawa, K. Nagasawa, A. Fukase, K. Higashiyama, S. Mori,
S. Yashiro, Y. Ishigaki, and H. Kanai, Proc. IEEE Int. Ultrason. Symp., 2020
, p. 1.
32) K. Nagasawa, A. Fukase, S. Mori, M. Arakawa, S. Yashiro, Y. Ishigaki, and
H. Kanai, J. Med. Ultrason. 48, 3 (2021).
33) H. Sakaki, M. Arakawa, S. Yashiro, Y. Todate, Y. ishigaki, and H. Kanai, J.
Med. Ultrason. 46, 3 (2019).
34) M. Arakawa, H. Sakaki, K. Nagasawa, A. Fukase, S. Mori, S. Yashiro,
Y. Ishigaki, and H. Kanai, Proc. IEEE Int. Ultrason. Symp., 2018, p. 1.
35) A. Fukase, K. Nagasawa, S. Mori, M. Arakawa, S. Yashiro, Y. Ishigaki, and
H. Kanai, IEEE Int. Ultrason. Symp., 2019, p. 45.
36) A. Fukase, K. Higashiyama, S. Mori, M. Arakawa, S. Yashiro, Y. Ishigaki,
and H. Kanai, Jpn. J. Appl. Phys. 60, SDDE08 (2021).
37) K. Higashiyama, S. Mori, M. Arakawa, S. Yashiro, Y. Ishigaki, and
H. Kanai, Proc. Symp. Ultrason. Electr. 42, 3Pa5 (2021).
38) P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGrawHill, New York, 1953), p. 1483.
39) Y. Hashimoto, N. Akashi, and J. Kushibiki, Proc. IEICE Tech. Rep., 1997,
p. 37.
40) B. I. Raju and M. A. Srinivasan, Ultrasound Med. Biol. 27, 1543 (2001).
41) B. E. Treeby, E. Z. Zhang, A. S. Thomas, and B. T. Cox, Ultrasound Med.
Biol. 37, 289 (2011).
42) R. Skalak, N. Ozkaya, and T. C. Skalak, Annu. Rev. Fluid Mech. 21, 167(1989).
43) M. L. Turgeon, Clinical Hematology: Theory and Procedures (Lippincott
Williams & Wilkins, Pennsylvania, 2005), p. 100.

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