REGULAR PAPER

Japanese Journal of Applied Physics 55, 07KF12 (2016)
http://doi.org/10.7567/JJAP.55.07KF12

Estimation of size of red blood cell aggregates using backscattering propertyof high-frequency ultrasound: In vivo evaluation
Yusaku Kurokawa1, Hirofumi Taki1,2*, Satoshi Yashiro3, Kan Nagasawa3, 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
The Department of Internal Medicine Division of Diabetes and Metabolism, Iwate Medical University, Morioka 020-8505, Japan2*E-mail: taki@ecei.tohoku.ac.jp; kanai@ecei.tohoku.ac.jp
Received November 14, 2015; accepted March 18, 2016; published online June 16, 2016
We propose a method for assessment of the degree of red blood cell (RBC) aggregation using the backscattering property of high-frequency
ultrasound. In this method, the scattering property of RBCs is extracted from the power spectrum of RBC echoes normalized by that from theposterior wall of a vein. In an experimental study using a phantom, employing the proposed method, the sizes of microspheres 5 and 20 µm in
diameter were estimated to have mean values of 4.7 and 17.3 µm and standard deviations of 1.9 and 1.4 µm, respectively. In an in vivo
experimental study, we compared the results between three healthy subjects and four diabetic patients. The average estimated scatterer diametersin healthy subjects at rest and during avascularization were 7 and 28 µm, respectively. In contrast, those in diabetic patients receiving both
antithrombotic therapy and insulin therapy were 11 and 46 µm, respectively. These results show that the proposed method has high potential forclinical application to assess RBC aggregation, which may be related to the progress of diabetes. © 2016 The Japan Society of Applied Physics

1.

Introduction

Medical ultrasound is widely and repetitively used for
diagnosis1–5) and treatment6–8) in clinical settings because
it is noninvasive and easy to use. For the diagnosis ofatherosclerosis, ultrasound imaging is used to observemorphological changes in the arterial wall. The conditionof blood is also an important marker for the diagnosis of
circulatory diseases such as atherosclerosis in the earlystage;9,10) however, noninvasive quantitative estimation of
the condition of blood is still challenging.
Red blood cells (RBCs) are the principal components ofblood, and several researchers have focused on the characteristics of the echo returned from RBCs.11,12) RBC aggregationis one of the primary determinants of blood viscosity,9,13) andit increases microvascular ﬂow resistance because of theadditional energy required for disaggregation at the beginning of microcirculation.14) Since excessive RBC aggregation
should impair microcirculation ﬂow, it may aggravate themicrovascular complications resulting from metabolic disorder.15) Furthermore, RBC aggregation deteriorates in subjects with diabetes, resulting from glycation of the surface
membrane protein in hemoglobin.16) In addition, excessive
RBC aggregation depresses shear stress on the vascularwall, and the depression of shear stress leads to endothelial
dysfunction and a characteristic change in the smooth muscleof the vascular wall.17,18) These phenomena increase therisk of thrombosis and atherosclerosis, and thus it is very
important to noninvasively assess RBC aggregation.
In the ﬁeld of ultrasound imaging, it is known thatsmokelike echoes occur during RBC aggregation.19) However, the assessment of RBC aggregation from the smokelike
echoes is qualitative. Therefore, it is necessary to evaluate
RBC aggregation quantitatively. Sato et al. have reported atechnique to estimate RBC aggregation using the ultrasonicpeak frequency, which they investigated in a basic experimental study using a silicone tube.20) Also, many papers
have reported on the assessment of the condition of blood.
Paeng and coworkers observed the variation of blood
echogenicity during the cardiac cycle.21,22) Calle and coworkers observed changes in the sound speed and scatterer

size on blood coagulation by in vitro measurement.23,24)
Franceschini et al. estimated the size of RBC aggregatesusing the structure factor size and attenuation estimator.25)
However, such studies required invasive processes.
In our previous study,26) we proposed a noninvasive
quantitative method for the assessment of RBC aggregation
using high-frequency ultrasound. RBC aggregation was
estimated by ﬁtting the measured power spectrum to one of
the theoretical power spectra of several scatterer sizes. Before
the ﬁtting process, the power spectrum of RBC echoes
was normalized by that of the posterior wall of the vein to
extract the scattering property. The echoes from the posteriorwall of the vein were measured in M-mode measurement.
Therefore, the signal-to-noise ratio (SNR) of the power
spectrum for the posterior wall of the vein was low because
the RF echoes were measured at a single location on theposterior wall of the vein.
In the present study, we improved the measurement
method and assessed its performance by in vivo experiment.
The proposed method improved the SNR of the reference
power spectrum by coherent integration and modiﬁcation of
the measurement conditions. In our previous study, thereference power spectrum from the posterior wall of a vein
was calculated from a single echo. In contrast, the proposed
method uses several echoes selected in B-mode measurement
to improve the SNR. The RF echoes from RBCs were
measured when the blood ﬂow was stopped by avascularization to induce a blood condition leading to RBC aggregation.
In our previous study, blood ﬂow was stopped by applying
pressure manually with a cuﬀ. However, the time required forcomplete avascularization varied. Therefore, an avascularization system was prepared using an air compressor with a
cuﬀ to measure all subjects under the same measurement
conditions. Furthermore, three healthy subjects and 26
diabetic patients were measured and the performance of the
proposed method was assessed.
2.

Materials and methods

2.1 Frequency characteristics of ultrasoundbackscattering from RBCs

The diameter of an RBC is about 8 µm, which is suﬃciently

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Y. Kurokawa et al.

for the measurement of the venous wall. In the present study,A2( f ) is assumed to be the same as A1( f ). We assume thatR( f ) is equal to a positive constant R0, that is, the reﬂection
property does not have frequency dependence because thevenous wall is assumed to be a ﬂat reﬂector. Therefore,
Eq. (2) can be rewritten as
10 log10

Ps ð f ÞjSð f Þj2
' 10 log10:
Pr ð f Þ
jR0 j2

ð3Þ

Therefore, the scattering properties of the scatterers, S( f ), canbe obtained by this normalization process, that is, Ps( f ) is
divided by Pr( f ).
Fig. 1. (Color online) Theoretical power spectrum log10[Q(ka)=4πa2] foreach scatterer diameter (2a).

small compared with the ultrasonic wavelength of 40 µm at
a frequency of 40 MHz. When the scatterer size is muchsmaller than the transmission wavelength, the frequency
spectrum of the echo from the scatterer follows Rayleigh’s
scattering law, where its power spectrum is proportional to
the fourth power of the frequency. In contrast, when the sizeof a scatterer is large, the scatterer is regarded as a reﬂector
and the power spectrum does not show frequency dependence. In this study, a scatterer was modeled by assuming
an inﬁnite number of inﬁnitesimal point sources on thesurface of a spherical scatterer.27) When a plane wave isirradiated to the scatterer, the theoretical power spectrum
Q(ka)=4πa2 of the scattered echo is given by28)1QðkaÞ X
2n þ 1 2 0¼
sin ½"n ðkaÞ&;2
2
4!an¼0 ðkaÞ

ð1Þ

where Q(ka) is the scattering cross section, k is the wave
number, a is the radius of the scatterer, n is the number ofpoint sources on the surface of the scatterer, and δAn(ka) is thederivative of the phase diﬀerence between the incident wave
and the scattered wave. The theoretical power spectrum
Q(ka)=4πa2 is given as a function of frequency f and scatterer
radius a (a ranges from 1 to 30 µm) by transforming ka into
2π(a=λ) = (2π=c)fa, where c is the acoustic velocity. Figure 1
shows the theoretical power spectrum for each scatterer
diameter 2a.
2.2

Normalization of power spectrum
The measured power spectrum Ps( f ) of the echoes from
RBCs of the dorsal hand vein depends not only on the
scattering properties of the scatterers, S( f ), but also on threeother factors: the frequency response of the transmitting andreceiving transducers, G( f ), the attenuation property of the
propagation medium, A1( f ), and the frequency spectrum
caused by the voltage applied to the transducer, X( f ). In thisstudy, the scattering properties of the aggregated RBCs wereextracted by normalization using the power spectrum Pr( f ) ofa ﬂat vein wall. This process is expressed by18)

Ps ð f ÞjSð f ÞGð f ÞA1 ð f ÞXð f Þj2¼ 10 log10
10 log10
Pr ð f ÞjRð f ÞGð f ÞA2 ð f ÞXð f Þj2

jSð f Þj2;
ð2Þ
jRð f Þj2
where R( f ) is the reﬂection property of the venous wall andA2( f ) is the attenuation property of the propagation medium' 10 log10

2.3

Calculation of reference power spectrum
In the proposed method, the reference power spectrum Pr( f )for in vivo measurement is calculated from the echoes fromthe lumen–intima interface of the posterior venous wall. The
echoes from a lumen–intima interface are sometimes unclear,and some of them are similar to the echo from a media–
adventitia interface. Since the reference power spectrumPr( f ) should be estimated from the echo that returned from asingle ﬂat interface, the above-mentioned cases should be
excluded.
In the present study, therefore, two processes were used:
one was the selection of ultrasonic echoes from a lumen–
intima interface located far from the echoes from a media–
adventitia interface, and the other was the improvement of
SNR by coherent integration. In the echo selection process,the ratio of the power of a center region to a tail region of
the RF echo is calculated and echoes with a high ratio are
selected. Figure 2 shows the RF echoes from a lumen–intima
interface and their frequency spectra. The width of thewindow function was equal to double the pulse width of theultrasound diagnostic equipment to extract the echo from thelumen–intima interface. When the extracted signal includes
only the RF echoes from a lumen–intima interface, as shownin Fig. 2(a), no dip in the power spectrum appears around thecenter frequency, as shown in Fig. 2(b). However, when amedia–adventitia interface is close to a lumen–intima interface, the signal extracted by the window function includes
part of the echo from the media–adventitia interface in the
tail region, as shown in Fig. 2(c), resulting in a small dip at afrequency of about 25 MHz in the power spectrum as shownin Fig. 2(d).
In the coherent integration process, we calculate the ratioof the power of a center region to that of a tail region foreach ultrasound beam, and we choose the RF echo with amaximum ratio as the reference echo. From the crosscorrelation between the reference echo and each of the otherRF echoes around the lumen–intima interface of other beams,
its time shift is determined. Each RF echo is shifted andaveraged, and the power spectrum is obtained.
2.4

Estimation of RBC aggregate size
We estimate the size of an RBC aggregate by ﬁtting themeasured RBC echo after the normalization process to thetheoretical echo based on Rayleigh scattering, where thediﬀerence between the measured frequency spectrum
10 log10[Ps( f )=Pr( f )] of Eq. (3) and the theoretical frequency
spectrum 10 log10[Q(ka)=4πa2] of Eq. (1) is minimized.18)
The minimization process is expressed by

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Y. Kurokawa et al.

Fig. 2. (Color online) (a) RF echo from lumen–intima interface. (b) Frequency spectrum of RF echo from lumen–intima interface. (c) RF echo from lumen–
intima interface and media–adventitia interface. (d) Frequency spectrum of RF echo from lumen–intima interface and media–adventitia interface.

N(11Xwð fk Þ½yð fk Þ ( y^ ð fk ; 2a; bÞ&2 ; ð4Þ
a;b N
k¼0

min "ða; bÞ ¼ mina;by^ ð fk ; 2a; bÞ ¼
wherey( f k) = 10 log10[Ps( f )=Pr( f )],10 log10 ½bQðkaÞ=4!a2 &, fk is the kth frequency, and w( fk)
is the weighting function.
In this study, the weighting function w( fk) was selected toemphasize the frequency component with high SNR. Since
the power spectrum Ps( f ) of the scattered echoes contains
noise components, the noise spectrum is compensated byusing the power spectrum Pnoise( f ) of RF echoes from thewater bywð fk Þ ¼ Ps ð f Þ ( Pnoise ð f Þ:

ð5Þ

Figure 3 shows the measured frequency spectrum after
normalization (red line), the weighting function w( fk) (blueline), and the theoretical frequency spectrum (green line) forthe estimated scatterer size of 12 µm. We prepared thetheoretical frequency spectrum for each of the scatterer
diameters 2a from 2 to 60 µm, that is, the scatterer radii a =1, 2, 3, …, 30 µm. RBC aggregation was estimated by ﬁtting
the measured power spectrum to each of the prepared theoretical power spectra. The estimated scatterer size was limited
from 2 to 60 µm.
2.5Basic experiments using microspheres
Ultrasound diagnostic equipment (Tomey UD-8000) with amechanical scan probe having a center frequency of 40 MHz
and a focal length of 9 mm was used. The RF echoes wereacquired at a sampling frequency of 240 MHz, and theirpower spectra were obtained by applying the Fourier

Fig. 3. (Color online) Measured normalized power spectrum log10[Ps( f )=Pr( f )], theoretical power spectrum log10[Q(ka)=4πa2], and weighting
function w( fk).

transform with a Hanning window of 0.15 µs (36 points) inlength.
Microspheres (Dantec Dynamics Polyamide Seeding
Particles) with diameters of 5, 20, and 50 µm were used.
The microsphere density was 2.0 g=l for the microsphereswith diameters of 5 and 20 µm. In contrast, it was 20.0 g=l
for the microspheres of 50 µm diameter because the numberof microspheres was not suﬃcient at a density of 2.0 g=l. To
disperse the microspheres, polyoxyethylene octylphenyl ether
was used as the surfactant. The measurement was repeated 15
times, where the ﬂuid was stirred during each measurement.
Therefore, the scatterer size was estimated 15 times for each

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Y. Kurokawa et al.

microsphere size. To eliminate the blocking eﬀect of
microspheres on the RF echo from a silicone plate, wemeasured the echo from the silicone plate located in water
without microspheres.
2.6

In vivo experiments
RBC aggregation occurs when the blood shear rate is
low.14,29,30) Therefore, we measured ultrasonic echoes from
RBCs with and without blood ﬂow, the blood ﬂow being
stopped by the application of pressure of about 250 mmHg
using a cuﬀ on the upper arm.
The measurement procedure was as follows. First, theposterior wall of the vein was set at the focus of the US device,
and RF echoes from a lumen–intima interface were acquired.
Then, the lumen of the vein was set at the focus, and RF
echoes from the RBCs were acquired while the subject was
at rest for 1 min and during avascularization for 2 min. The
power spectrum Ps( f ) of the echoes from RBCs wascalculated by averaging 339 power spectra of RF echoes,
three echoes from each of the 113 scan lines being extracted.
The diﬀerence in RBC aggregation between at rest and during
avascularization was evaluated. In this study, we created anavascularization system using an air compressor and a cuﬀ tomeasure several subjects under the same conditions.
We applied this method to three healthy subjects and 26
diabetic patients including four patients receiving both
antithrombotic therapy and insulin therapy in the clinicalstudy. Each healthy subject was measured three times on
diﬀerent days. Each diabetic patient was measured once.
This research was approved by the Ethics Committee forClinical Research at Graduate School of Engineering,Tohoku University, and that at Iwate Medical University.
Measurements were conducted only after obtaining written
informed consent following an explanation of the study
content to the subjects.
3.

Fig. 4. (Color online) (a) Power spectra Ps( f ) of the ultrasonic echoesfrom the microspheres. (b) Power spectrum Pr( f ) of the ultrasonic echoesfrom the silicone plate.

Results

3.1

Basic experiments using microspheres
Figure 4 shows the average power spectra of the microsphereechoes and that of the echoes from the silicone plate. The
microsphere size was estimated by ﬁtting the measured
power spectrum to each of the theoretical power spectra forthe 30 scatterer sizes.
As shown in Fig. 4(a), the power spectrum of the 50 µm
echo has a dip at a frequency of about 25 MHz. This might
have originated from the resonance of 50 µm microspheres.
The dip in the power spectrum caused a negative slope withrespect to frequency after normalization. Since the theoreticalpower spectrum has a positive slope, the proposed method
failed to estimate the size of the 50 µm microspheres. Therefore, we estimated the sizes of the 5 and 20 µm microspheres
using the proposed method as follows.
Figure 5 shows the measured power spectra after normalization using the reference power spectrum from the silicone
plate shown in Fig. 4(b), the theoretical power spectra forthe estimated scatterer diameters, and the weighting function.
In this measurement, the diameters of the 5 and 20 µm
microspheres were estimated to be 6 and 18 µm, respectively.
Each measured power spectrum is close to the theoretical one
in the frequency band from 30 to 50 MHz, where eachweighting function has a large value.

Fig. 5. (Color online) Measured normalized power spectra log10[Ps( f )=Pr( f )] of microspheres, theoretical power spectra log10[Q(ka)=4πa2]
corresponding to the estimated scatterer diameters, and weighting functionw( fk).

Figure 6 shows the mean values and standard deviations of
the estimated scatterer diameters of 5 and 20 µm. The meanvalues were 4.7 and 17.3 µm and the standard deviations were
1.9 and 1.4 µm, respectively.
3.2

In vivo measurements
The diameter of an RBC is about 8 µm. We set the lower andupper limits for the estimated scatterer sizes as 4 and 50 µm,
respectively. Figure 7 shows a B-mode image of the RF
echoes acquired from the posterior wall of a vein. As
described in Sect. 2.3, we selected beams with echoes froma lumen–intima interface located far from the echoes from a
media–adventitia interface.
Figure 8 shows a comparison among the frequency spectraof the echoes from the posterior wall of the vein. Using the07KF12-4© 2016 The Japan Society of Applied Physics

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Y. Kurokawa et al.

Fig. 6. (Color online) Mean values and standard deviations of theestimated scatterer diameters of 5 and 20 µm.

Fig. 7. (Color online) B-mode image of RF echoes from the posteriorwall of a vein at the dorsum manus.

conventional process, the spectrum in Fig. 8(a) was calculated using all echoes from the posterior wall of the vein, as
expressed by
E bjF½yðtÞ&j2 c;

8beamsð6Þ

where F denotes the Fourier transform and [y(t)] denotes RF
echoes from the posterior wall of the vein. When multiple
broad-band echoes return from diﬀerent depths, dips appear
in the frequency spectrum of the received signal at thefrequency determined by the interference between echoes.
The conventional process extracted the echo from the lumen–
intima interface, which is overlaid by the echo from themedia–adventitia interface, resulting in the appearance of a
dip at 25 MHz in the frequency spectrum.
Figure 8(b) shows the spectrum obtained using theselected echoes from the lumen–intima interface, as expressed byE

bjF½yðtÞ&j2 c:well separated beams

ð7Þ

Figure 8(c) shows a comparison of the reference spectra
obtained by incoherent integration and coherent integration.
The red spectrum in Fig. 8(c) is the same as the average
spectrum in Fig. 8(b). The blue spectrum in Fig. 8(c) was
obtained by the coherent integration process, as expressed by
!
!2
!
!
E
½F½yðt ( #i Þ&&! ;ð8Þ!
beam i 2 fwell separated beamsg

where τi is the time shift determined for the ith beam number.

Fig. 8. (Color online) Averaged power spectrum for the reference echo,
where each error bar shows the standard deviation. (a) Conventionalreference power spectrum Pr( f ) averaged among all beams. (b) Reference
power spectrum Pr( f ) averaged among the selected beams. (c) Comparisonof the reference power spectra Pr( f ) calculated by incoherent integration andcoherent integration after beam selection.

Figures 9 and 10 show the B-mode images of the dorsum
vein of a 23-year-old healthy subject (subject A) and those ofa diabetic patient (subject G), respectively. In the diabetic
patient, the echo intensity in the lumen at rest [Fig. 10(a)] is
higher than that in the healthy subject at rest [Fig. 9(a)], andalmost the same as that of the healthy subject during
avascularization [Fig. 9(b)].
Figures 11(a) and 11(b) respectively show the frequency
spectra of the echoes from RBCs in the three healthy subjects(healthy A, B, C) and the four diabetic patients (patients D, E,
F, G) that received both antithrombotic therapy and insulin
therapy. The echo intensity of the RBCs increases upon
avascularization using a cuﬀ. This result shows that RBC
aggregation resulted from avascularization. Table I shows thediﬀerence in the power at the center frequency from 10 and
60 MHz. The diﬀerence is signiﬁcantly diﬀerent between thehealthy subjects and diabetic patients.
Figure 12 shows the power spectra of the echoes from thelumen–intima interface for each subject. In the present study,
we improved the method of calculating reference power

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Y. Kurokawa et al.

Fig. 9. (Color online) Healthy subject’s B-mode images of RF echoesfrom the lumen during (a) rest and (b) avascularization.

Fig. 10. (Color online) Diabetic patient’s B-mode images of RF echoesfrom the lumen during (a) rest and (b) avascularization.

Fig. 11. (Color online) Power spectra of the echoes from RBCs for (a) healthy subjects (healthy A, B, C) and (b) diabetic patients (patients D, E, F, G).

Table I. Diﬀerence in the power of the power spectrum Ps( f ) at the center frequency for each subject.
Subject

From 10 MHz at rest(dB)

From 60 MHz at rest(dB)

From 10 MHz during
avascularization(dB)

From 60 MHz during
avascularization(dB)

Healthy A

11.2

6.6

17.3

14.3

Healthy B

11.8

7.0

16.0

13.0

Healthy C

9.4

4.0

13.2

9.2

Patient D

21.8

12.8

19.3

18.0

Patient E

19.8

13.0

20.0

19.9

Patient F

23.1

16.2

21.7

21.8

Patient G

20.6

12.5

23.1

20.5

spectra. As a result, dips in the power spectra weresuccessfully excluded in all subjects as shown in Fig. 12.
Figure 13 shows the measured normalized power spectra
and the theoretical power spectra for the estimated scatterer
diameters for healthy subject A. Figures 14 and 15 show thetransient changes in the estimated scatterer diameters for thethree healthy subjects (healthy A, B, C) and the four diabetic
patients (patients D, E, F, G), respectively. Since eachdiabetic patient was measured once owing to ethicalconsiderations, Fig. 15 has no error bars. In the healthy
subjects, the scatterer diameters at rest ranged from 4 to12 µm, close to that of non-aggregated RBCs. On the other
hand, the scatterer diameters during avascularization werelarger than those at rest, showing that the proposed method
succeeded in estimating the RBC aggregation originatingfrom avascularization. The averages of the estimated scatterer

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Y. Kurokawa et al.

Fig. 12. (Color online) Power spectra Pr( f ) of the echoes from theposterior wall of the vein of the seven subjects.
Fig. 15. (Color online) Transient changes in average estimate scatterer
diameters during a 3 min period for four diabetic patients.

Fig. 13. (Color online) Normalized power spectra log10[Ps( f )=Pr( f )],theoretical power spectra log10[Q(ka)=4πa2] corresponding to the estimatedscatterer diameters, and weighting functions w( fk).

Fig. 14. (Color online) Transient changes in average estimated scatterer
diameters with standard deviations during a 3 min period obtained by three
in vivo measurements of three healthy subjects.

diameters in the healthy subjects at rest (0 to 60 s) and during
avascularization (70 to 180 s) were 7 and 28 µm, respectively.
In contrast, those in the diabetic patients receiving both
antithrombotic therapy and insulin therapy were 11 and46 µm, respectively.
Figure 16 shows the average scatterer diameter of 26
diabetic patients (a) at rest and (b) during avascularization
estimated by the proposed method plotted against HbA1c,
an indicator used in diabetic control. A diabetes specialist
graded the 26 patients from 1 (mild) to 3 (severe) according
to the severity of their diabetes based on vascularcomplications resulting from diabetes. We eliminated threepatients with type I diabetes and two inpatients with type II
diabetes from the 26 patients, and classiﬁed the remaining 21

Fig. 16. (Color online) Average scatterer diameter of 26 diabetic patients(a) at rest and (b) during avascularization estimated by the proposed method
plotted against HbA1c, an indicator used in diabetic control.

patients into three groups: patients without any antithrombotic therapy or insulin therapy (red), patients receiving
insulin therapy only (green), and patients receiving both
antithrombotic therapy and insulin therapy (blue). The bluegroup is considered to comprise patients with the most severe
diabetes. During avascularization, the estimated scatterer
diameter of the group receiving both antithrombotic therapy

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and insulin therapy (blue) was larger than those of the othertwo groups as shown in Fig. 16(b). This ﬁnding shows that
RBC aggregation depends on the severity of diabetes.
4.

Conclusions

We have herein proposed a method by which the degree of
red blood cell (RBC) aggregation can be assessed using thescattering property of RBCs. In basic experiments in vitro,the sizes of microspheres 5 and 20 µm in diameter were
estimated to be 4.7 and 17.3 µm, respectively, by the
proposed method. In in vivo measurements, RF echoes from
RBCs at the dorsum manus of healthy subjects and diabetic
patients were measured. The measurement was performed
while the subject was at rest for 1 min and during avascularization for 2 min, and the estimated scatterer diameters during
avascularization were larger than those at rest. The estimatedscatterer diameters of diabetic patients at rest did not always
diﬀer from those of healthy subjects, which suggests that weshould reconsider the theoretical model and the evaluation
method. However, during avascularization, the average
scatterer diameter of healthy subjects and that of diabetic
patients receiving both antithrombotic therapy and insulin
therapy were 28 and 46 µm, respectively. This ﬁnding showsthat RBC aggregation depends on the severity of diabetes.
The power spectra of the echoes from RBCs were diﬀerent
between healthy subjects and diabetic patients, showing thatthe estimation accuracy in RBC aggregation can be improvedby taking into account the intensity of the power spectrum inthe future. These results show the high potential of this novel
diagnostic technique for estimating RBC aggregation in
cardiovascular diseases using high-frequency ultrasound.
Acknowledgment

This work was partly supported by MEXT=JSPS KAKENHI
Grant Number 26630178.

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