Reprinted from

REGULAR PAPER

Estimation of Scatterer Diameter by Normalized Power Spectrum of High-Frequency
Ultrasonic RF Echo for Assessment of Red Blood Cell Aggregation
Taku Fukushima, Hideyuki Hasegawa, and Hiroshi Kanai

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REGULAR PAPER

Japanese Journal of Applied Physics 50 (2011) 07HF02
DOI: 10.1143/JJAP.50.07HF02

Estimation of Scatterer Diameter by Normalized Power Spectrum of High-Frequency
Ultrasonic RF Echo for Assessment of Red Blood Cell Aggregation
Taku Fukushima1 , Hideyuki Hasegawa2;1 , and Hiroshi Kanai1;2 
12Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan

Received December 13, 2010; accepted March 1, 2011; published online July 20, 2011
Red blood cell (RBC) aggregation, as one of the determinants of blood viscosity, plays an important role in blood rheology, including the conditionof blood. RBC aggregation is induced by the adhesion of RBCs when the electrostatic repulsion between RBCs weakens owing to increases inprotein and saturated fatty acid levels in blood, excessive RBC aggregation leads to various circulatory diseases. This study was conducted toestablish a noninvasive quantitative method for assessment of RBC aggregation. The power spectrum of ultrasonic RF echoes fromnonaggregating RBCs, which shows the frequency property of scattering, exhibits Rayleigh behavior. On the other hand, ultrasonic RF echoesfrom aggregating RBCs contain the components of reflection, which have no frequency dependence. By dividing the measured power spectrum of
echoes from RBCs in the lumen by that of echoes from a posterior wall of the vein in the dorsum manus, the attenuation property of the
propagating medium and the frequency responses of transmitting and receiving transducers are removed from the former spectrum. RBC
aggregation was assessed by the diameter of a scatterer, which was estimated by minimizing the square difference between the measured
normalized power spectrum and the theoretical power spectrum. In this study, spherical scatterers with diameters of 5, 11, 15, and 30 m were
measured in basic experiments. The estimated scatterer diameters were close to the actual diameters. Furthermore, the transient change of thescatterer diameters were measured in an in vivo experiment with respect to a 24-year-old healthy male during the avascularization using a cuff.
The estimated diameters (12–22 m) of RBCs during avascularization were larger than the diameters (4–8 m) at rest and after recirculation.
These results show the possibility of the use of the proposed method for noninvasive assessment of RBC aggregation.
# 2011 The Japan Society of Applied Physics

1. Introduction

Medical ultrasound is clinically used to make a diagnosis forvarious organs, and it can be repeatedly employed to conﬁrm
time-dependent changes because it is noninvasive andpatients have less stress. For diagnosis of atherosclerosis,
ultrasound imaging is widely used for morphologicalobservation of the arterial wall. Furthermore, methods forevaluating the viscoelasticity of the arterial wall haverecently been developed.1,2)
As well as the morphology and viscoelasticity of thearterial wall, the condition of blood is also a useful marker
for the diagnosis of atherosclerosis.3,4) However, conventional ultrasonic images cannot be applied to evaluate thecondition of blood because red blood cells (RBCs), which
are the main components of blood, are much smaller than
the wavelength of the ultrasound and the diﬀerence inacoustic impedance between blood plasma and RBCs is verysmall.
RBC aggregation, as one of the determinants of blood
viscosity, plays an important role in the condition ofblood.3,5) The tunica adventitia of healthy RBCs is charged
with negative electricity, which impedes RBC adherence byelectrostatic repulsion.6) However, due to the increase in theadhesive force of high-molecular substances such as protein,saturated fatty acid, and cholesterol in blood serum, the forceof electrostatic repulsion between RBCs is weakened. As aresult, RBC aggregation easily occurs.7)
RBCs play a role to carry oxygen and nutritive components to all parts of the body. RBC aggregation degrades
such ability of RBCs.8) Therefore, excessive RBC aggregation becomes a factor for diabetes and hyperlipidemia
because less protein and lipid are chronically carried foreach organ.9,10) In addition, RBC aggregation increases
blood viscosity7) and, therefore, the excessive RBC aggregation also becomes a factor for thrombosis and atherosclerosisE-mail address: kanai@ecei.tohoku.ac.jp

because the increase of blood viscosity leads to themorphological change of vascular wall such as theendothelial dysfunction and the characteristic change ofsmooth muscle.11,12) Consequently, assessment of RBC
aggregation is essential.
The microchannel array ﬂow analyzer (MC-FAN) method
is a recently developed technique for evaluating thecondition of blood by observation of whether red blood
cells pass through gaps in silicon substrates simulating blood
capillaries.13) However, this method is not quantitative.
Furthermore, the blood is collected with a syringe andmeasured after administration of anticoagulant, i.e., invasive, results being inﬂuenced by such collection and theamount of administered anticoagulant. Many studies on
assessment of RBC aggregation in various organs have beenreported. Shung et al. observed blood echogenicity variation
during the cardiac cycle.14,15) Lizzi et al. showed that sizesof scatterers in tissue could be estimated from the spectral
slope.18) However, these methods and studies are invasive
due to collection of blood as well as employment of the
MC-FAN method. Furthermore, Cloutier et al. estimatedblood structure parameters relating to scatterer size,
attenuation, and scattering cross section of the backscattering coeﬃcient in in vivo measurement.16,17) However, thesize of aggregated RBCs have not yet been estimated inin vivo measurements. The purpose of the present study wasto establish a noninvasive quantitative method for assessment of RBC aggregation.
In our previous study,4) RBC aggregation was assessed byestimating the spectral slope. However, the calculation of thespectral slope requires application of a high-pass ﬁlter which
decreases the estimation accuracy of scatterer diameter andincreases the inﬂuence of random noise including echoes.
Furthermore, the attenuation property of the propagation
path was not completely removed in the estimation of thespectral slope. In addition, although some researchers haveestimated scatterer size and the attenuation property fornormalization,18,19) noninvasive estimation of scatterer

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T. Fukushima et al.
theoretically scattered power spectrum

diameter by removing the attenuation property of the
propagating medium for normalization is diﬃcult due toinhomogeneous tissues with unknown attenuation properties.
For dealing with this problem, we improved the method fornormalization of the measured power spectrum and developed a new method to estimate scatterer diameter from thenormalized power spectrum.
2. Principles
2.1 Theoretical power spectrum of scattered echoes

where QðkaÞ 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 0n ðkaÞ is thederivation of the phase diﬀerence between the incident wave
and the scattered wave.
Figure 1 shows the theoretical power spectrum QðkaÞ=a2 as a function of ka. Furthermore, the power spectrumQðkaÞ=a2 is also given as a function of frequency ( f )and scatterer radius (a) by transforming ka ¼ 2ða=Þ ¼
ð2=cÞf a, where c is the acoustic velocity. Therefore,
logarithmic theoretical power spectra log10 QðkaÞ=a2 at
diﬀerent scatterer radii as a function of frequency ( f ) are
shown in Fig. 2.
2.2 Normalization in power spectrum

The power spectrum of ultrasonic RF echoes fromnonaggregating RBCs exhibits Rayleigh behavior.21,22) It is
well known that the power spectrum Ps ð f Þ of the scatteredwave is proportional to the fourth power of frequency. On
the other hand, ultrasonic RF echoes from aggregating RBCs
contain the components of reﬂection, which have nofrequency dependence. Therefore, the spectral slope decreases when scatterer size increases and the components ofreﬂection are included in the echoes.23)
The measured spectrum Zs ð f Þ of the received ultrasonicecho signal es ðtÞ contains the scattering property Sð f Þ fromscatterers, the frequency response Gð f Þ of transmitting andreceiving transducers, and the attenuation property A1 ð f Þ ofthe propagating medium. In summary, the measured
spectrum Zs ð f Þ is given byZs ð f Þ ¼ Sð f ÞGð f ÞA1 ð f Þ  Xð f Þ;

ð2Þ

1.2
1
0.8
0.6
0.4
0.2
0

0

1

2

3

4

5

ka
Fig. 1. (Color online) Theoretical power spectrum QðkaÞ=a2 of ascattered echo.

logarithmic power spectrum

An RBC is a very small ultrasonic scatterer whose diameteris 8 m at most. In addition, the diﬀerence between acoustic
impedance of blood plasma and that of an RBC is verysmall; thus, the amplitudes of scattered RF echoes are verysmall. Therefore, the power spectrum of the echoes from
RBCs is calculated using the fast Fourier transform (FFT) toevaluate in the frequency domain because the scattering
properties of RF echoes are various, corresponding toscatterer size. In addition, it was assumed that the diameterof a scatterer increases depending on the degree of RBC
aggregation.
In the present study, a scatterer was modeled by placing
an inﬁnite number of inﬁnitesimal point sources on thesurface of the scatterer. When a plane wave insoniﬁes thescatterer, the theoretical power spectrum QðkaÞ=a2 of thescattered echo is given by20)
1
X
QðkaÞ
2n þ 1 2 0¼
4
sin ½n ðkaÞ;
ð1Þ
2
2
a
n¼0 ðkaÞ

1.4

1
0.5
0
−0.5
−1
−1.5
−2
−2.5
−3
−3.5
10

4 µm
8 µm
12 µ m16 µ m20 µ m24 µ m32 µ m40 µ mscatterer
diameter (2a)2030frequency ( f ) [MHz]4050

Fig. 2. (Color online) Logarithmic theoretical power spectrum
log10 QðkaÞ=a2 with constant values in each scatterer diameter (2a).

where Xð f Þ is the spectrum of the transmitted signal. The
normalization of the power spectrum has been introduced bysome researchers.24,25) Cloutier et al. removed the frequency
response Gð f Þ of the transmitting and receiving transducer.16) However, the attenuation property A1 ð f Þ of the
propagation medium is diﬃcult to remove under in vivo
conditions because the propagation medium in in vivo
measurements is inhomogeneous tissue with unknown
attenuation properties.
Therefore, in the present study, the power spectrum Pr ð f Þof ultrasonic RF echoes from the posterior wall of thevein was used for normalization because the propagation
media in the measurements of the posterior wall and in themeasurements of RBCs in the lumen of the vein are similarso that not only the frequency response Gð f Þ of thetransducer but also the attenuation property A1 ð f Þ of the
propagation medium can be removed. Therefore, normalization is performed as bellow:
10 log10

Ps ð f Þ
jZs ð f Þj2¼ 10 log10
Pr ð f Þ
jZr ð f Þj2
jSð f ÞGð f ÞA1 ð f Þ  Xð f Þj2
jRð f ÞGð f ÞA2 ð f Þ  Xð f Þj2
jSð f Þj2
 10 log10;
ð3Þ
jRð f Þj2
¼ 10 log10

where Rð f Þ is the reﬂecting property and A2 ð f Þ is theattenuation property of the propagating medium in themeasurement of echoes from the posterior wall of the vein.

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T. Fukushima et al.

(a) 2

window lengthnormalized logarithmic
power spectrum

amplitude [V]

1
0.5
0
−0.5

10.4

10.6

10.8
time [µs]11−2experimental power
theoretical power (4 µ m)

10

20
30
frequency [MHz]

40

50

20
30
frequency [MHz]

40

50

(b) 1
weighting function

the posterior wall obtained by compressing the vein.

power spectrum [dB]

−1

11.2

Fig. 3. (Color online) RF echoes from RBCs in the lumen of the vein and

−30

0

−3

RBCs in the lumen
posterior wall

−1

1

RBCs in the lumen
posterior wallPs ( f )Pr ( f )

−40
−50

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
10

−60
Fig. 5. (Color online) (a) Measured normalized logarithmic power
spectrum log10 Ps ð f Þ=Pr ð f Þ and logarithmic theoretical power spectrum
log10 QðkaÞ=a2 shifted in the vertical direction at scatterer diameter of
4 m. (b) Weighting function wð fk Þ obtained from MSCF among theultrasonic echoes scattered from RBCs in the lumen using same echoes as
Fig. 5(a).

−70
0

20

40
60
frequency [MHz]

80

100

Fig. 4. (Color online) Power spectra of the ultrasound echoes reﬂectedfrom the posterior wall and scattered from RBCs in the lumen.

Figure 3 shows RF echoes reﬂected by the posterior wall
(blue line) and scattered from RBCs (red line) in the lumen.
RF echoes reﬂected by the posterior wall include echoesfrom the tissues under the posterior wall and RBCs in
the lumen. Such undesirable echoes were suppressed byapplying a Hanning window centered at the central time ofan echo from the posterior wall (10.8 s) before the Fouriertransform was performed. Window length was 0.256 s,which corresponds to the pulse duration of the echo fromthe posterior wall. Figure 4 shows the power spectrum Pr ð f Þfrom the posterior wall and the power spectrum Ps ð f Þ from
RBCs in the lumen. Each power spectrum in Fig. 4 was
obtained by averaging 1000 power spectra of RF echoes toreduce the inﬂuences of dips originating from the interference of particular echoes scattered from RBCs.
2.3 Estimation method of scatterer size using weighting
functionIn the present study, scatterer size was estimated bydetermining the theoretical power spectrum log10 QðkaÞ=a2 , which minimized the diﬀerence between the measured
normalized power spectrum log10 Ps ð f Þ=Pr ð f Þ and theoretical power spectrum log10 QðkaÞ=a2 shown in Fig. 2. Let
us deﬁne the square diﬀerence () between the measured
normalized power spectrum log10 Ps ð f Þ=Pr ð f Þ and thetheoretical power spectrum log10 QðkaÞ=a2 as follows:1X
1N^ fk ; 2aÞ þ bg2 ;wð fk Þ2 fyð fk Þ  ½ yð
ð4Þ
¼
N k¼0

where yð fk Þ is the measured normalized logarithmic power^ fk Þ is the
spectrum log10 Ps ð fk Þ=Pr ð fk Þ at a frequency of fk , yðlogarithmic theoretical power spectrum log10 QðkaÞ=a2 , fk
is the discrete frequency, b is the intercept of the theoreticalpower spectrum, and wð fk Þ is the weighting function.
In this study, by considering the signal-to-noise ratio(SNR) of the echo at each discrete frequency, the weighting
function wð fk Þ was deﬁned by the magnitude-squared
coherence function (MSCF) jð fk Þj2 as follows:26)
wð fk Þ ¼ jð fk Þj2 ¼

jEn ½Yn ð fk ÞYnþ1 ð fk Þj2;
En ½jYn ð fk Þj2   En ½jYnþ1 ð fk Þj2 

ð5Þ

where Yn ð fk Þ is power spectrum in each beam from RBCs in
the lumen, En ½ is the averaging operation for the frames, is the complex conjugate, and n is the frame number.
Figure 5(a) shows measured normalized logarithmic
power spectrum log10 Ps ð fk Þ=Pr ð fk Þ (red solid line) andlogarithmic theoretical power spectrum log10 QðkaÞ=a2(green solid and dashed lines) at a scatterer radius a of
4 m, and Fig. 5(b) shows the weighting function wð fk Þ
obtained from the same ultrasonic echoes shown in Fig. 5(a),which were scattered from RBCs in the lumen. In this study,
we deﬁne the weighting function wð fk Þ obtained from MSCF
among received RF echoes from RBCs of the lumen to
consider the SNR of echoes from RBCs, which is the signalof interest. As shown in Fig. 5(a), for each size (diameter)of scatterers, the diﬀerence between the measured andtheoretical power spectrum was minimized by changing
the intercept (b) of the theoretical power spectrum. As aconsequence, scatterer radius is estimated to be the size
giving the smallest sum of the square diﬀerence .

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Table I. Particle diameters, properties, and polymer materials of eachmicrosphere.

Speciﬁcgravity

Volumefraction
(%)

(1)

52

1.10

0.0910(2)

11  31.00

0.1000(3)

15  51.11

0.0901(4)30  101.00

0.1000power spectrum [dB]

Particle diametermean  SD(m)(a) −20

Polymermaterial
Acrylic nitrile,
vinylidene chloride
Acrylic nitrile
Acrylic nitrile,
vinylidene chloride
Acrylic nitrile

No. (1)
No. (2)
No. (3)
No. (4)

−30
−40
−50
−60
−70
0

20

40
60
frequency [MHz]

80

100

power spectrum [dB](b) −20

3. Basic Experiments Using Microspheres

Ultrasound diagnostic equipment (Tomey UD-1000)
equipped with a mechanical scan probe at a center frequency
f0 of 40 MHz (wavelength is about 40 m) was used for
acquiring ultrasonic echo signals. The RF echoes wereacquired at a sampling frequency of 1 GHz at a 8-bit
resolution by an oscilloscope (Tektronix DPO7054), andtheir power spectra were obtained by applying the fast
Fourier transform with a Hanning window of 0.256 s inlength. In the present study, 768 zero points were added sothat signal length for Fourier analysis became 1.024 s to
improve the frequency resolution.
Table I shows the sizes and properties of the measured
microspheres. The shells of microspheres (1) and (3) weremade of copolymer including acrylic nitrile and vinylidene
chloride with Cl2 , and microspheres (2) and (4) were madeof copolymer including acrylic nitrile without Cl2 . In
addition, the liquid hydrocarbon is included inside eachmicrosphere. Microspheres of diﬀerent sizes, which weremixed with water at a density of 1.00 g/l, simulated
nonaggregated RBCs and aggregated RBCs. This density
is lower than that of RBCs in actual blood to prevent theconcentration of microspheres.
In addition, RF echoes from a silicone plate, which wasused as a reﬂector, were measured with microspheres in thewater at the same density as the measurement of RF echoesfrom the microspheres. Inﬂuences of the diﬀerence between
acoustic impedances of microspheres and RBCs was notconsidered in the present study.
Figure 6(a) shows the averaged power spectrum Ps ð f Þ ofechoes from each microsphere. Figure 6(b) shows theaveraged power spectrum Pr ð f Þ of echoes from the silicone
plate in the water with each microsphere. The numbers
correspond to the microsphere numbers in Table I. In thebasic experiments, microspheres with and without Cl2 wereused as a scatterer. Therefore, the acoustic properties may bevaried by adding Cl2 . Actually, as shown in Fig. 6(a), themagnitude of the power spectrum Ps ð f Þ of echoes from alarger sphere is not always greater than that from a smaller
sphere, which suggests that the acoustic impedance may bevaried by Cl2 . However, in the present study, scatterer
diameters are not estimated from the magnitude of the power
spectra Ps ð f Þ, but from the frequency properties corresponding to the slope of the normalized power spectrum
log10 Ps ð f Þ=Pr ð f Þ, so that the estimation of the scatterer
diameters is less inﬂuenced by the existence of Cl2 inthe shells. Furthermore, to acquire echoes from various

−30
−40
−50
−60

No. (1)
No. (2)
No. (3)
No. (4)

−70
−80

0

20

40
60
frequency [MHz]

80

100

Fig. 6. (Color online) (a) Power spectra Ps ð f Þ of the ultrasonic echoesfrom the microspheres (1)–(4) in Table I. (b) Power spectra Pr ð f Þ of theultrasonic echoes from the silicone plate with microspheres (1)–(4) in thewater.

statistically diﬀerent spatial distribution of spheres, RFechoes from the microspheres were measured by manuallystirring microspheres to keep a certain ﬂow rate.
Figure 7(a) shows the logarithmic normalized power
spectra log10 Ps ð f Þ=Pr ð f Þ (solid line) and the logarithmic
theoretical power spectra log10 QðkaÞ=a2 (dashed line) corresponding to the estimated scatterer diameters. Figure 7(b)shows the weighting functions wð fk Þ for each microsphere.
As shown in Fig. 7, the normalized power spectra
log10 Ps ð f Þ=Pr ð f Þ show high values at the frequency range
around 10 MHz. As shown in Figs. 6(a) and 6(b), the power
spectra Ps ð f Þ, Pr ð f Þ of echoes from the microsphere andthe silicone plate show similar and low magnitude in afrequency range less than 10 MHz because RF echoes hardly
contain such frequency components. Therefore, the normalized power spectrum log10 Ps ð f Þ=Pr ð f Þ shows around
0 dB and the weighting function wð fk Þ obtained from theechoes scattered from microspheres shows low values at
the frequency range less than 10 MHz due to low SNRs.
However, the power spectrum Pr ð f Þ of echoes from thesilicone plate shows high magnitudes compared with thepower spectrum Ps ð f Þ of echoes from the microsphere in therange from 20 to 40 MHz, which corresponds to the width at
half maxima of power spectrum, because the amplitude ofthe echoes from the silicone plate shows high compared withthat of the echoes from the microsphere. Therefore, thenormalized power spectrum log10 Ps ð f Þ=Pr ð f Þ shows negative values. Consequently, the normalized power spectrum
log10 Ps ð f Þ=Pr ð f Þ, which calculated by dividing the power
spectrum Pr ð f Þ of the echoes obtained from the silicone
plate by the power spectrum Ps ð f Þ of the echoes obtained
from microsphere, show high values at the frequency range
less than 10 MHz.

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normalized logarithmic
power spectrum(a) 1.5

T. Fukushima et al.
Table II. Particle diameters and experimental estimated results of eachmicrosphere.

4 µm
10 µ m16 µ m24 µ m

1
0.5
0
−0.5

No. (1)
No. (2)
No. (3)
No. (4)

−1
−1.5

(b)

1

weighting function

−2
10

0.8

20
30
frequency [MHz]4050Particlediametermean  SD(m)

Estimated scatterer
diametermean  SD(m)Maximum
and minimum values
in the 10 measurements
(m)

(1)

52

6:8  3:7

4–14

(2)
(3)

11  315  5

8:7  4:8
15:1  2:9

4–16
8–18

(4)

30  1030:6  7:9

18–40

(a)

20 ms

1.0 mm0.6
focus

window
length0.4
No. (1)
No. (2)
No. (3)
No. (4)

0.2
0

0

20

40
60
frequency [MHz]

(b)
80

100

20 ms

1.0 mmFig. 7. (Color online) (a) Normalized power spectra Ps ð f Þ=Pr ð f Þ ofmicrospheres (1)–(4) in Table I and logarithmic theoretical power spectra
log10 QðkaÞ=a2 corresponding to the estimated scatterer diameters. (b)Weighting function wð fk Þ obtained from MSCF among the ultrasoundechoes scattered from microspheres (1)–(4) in Table I (solid line) andscattered from RBCs in the lumen of the vein (dashed line).

focus

(c)

window
length20 ms

1.0 mmAs shown in Fig. 7(a), there are large dips in thenormalized power spectra log10 Ps ð f Þ=Pr ð f Þ. These dips
are considered to be occurred by the interference of echoesfrom the surface and other particular positions such as insideof the silicone plate, which were included in the window
for the frequency analysis because the RF echoes reﬂectedfrom silicone plate are acquired from the same ﬁxed beam.
As shown in Fig. 7(b), the weighting functions are
considered to show large values between 50 and 90 MHz
due to the inﬂuence of the multiple scattering among
microspheres caused by strong scattering of microspheres
unlike RF echoes from RBCs in the lumen. However, thevalue of the weighting functions wð fk Þ decreased at about
50 MHz in all microspheres. In addition, the frequency range
applied for normalization was limited because of using theultrasonic pulse, which has a ﬁnite frequency bandwidth. In
the present study, therefore, the normalized power spectrum
log10 Ps ð f Þ=Pr ð f Þ in the frequency range from 10 to 50 MHz
was used to estimate the scatterer diameters.
The Table II shows the mean and the standard deviation,and the maximum and minimum of the estimated scatterer
diameters for ten measurements of each microsphere.
Although some of the estimated scatterer diameters werebeyond the actual scatterer diameters, as shown in the lefthand column of Table II, estimated scatterer diameters areapproximately true values.
4. In vivo Experiments

RBCs in blood do not aggregate in large blood vessels
because of high blood shear rate.27–29) In this study, tofocus

window
lengthFig. 8. (Color online) M-mode images of RF echoes from the focal point
positioned in the lumen of the vein at the dorsum manus: at rest (a), during
avascularization (b), and after recirculation (c).

measure ultrasonic echoes from the blood, a condition whichtends to occur in aggregated RBCs, blood ﬂow was stopped
by applying pressure with a cuﬀ surrounding the upper arm
at 250 mmHg. Ultrasonic echoes were acquired at rest for
2 min, during avascularization for 5 min, and after recirculation for 3 min. Figure 8 shows M-mode images of 1000 RF
echoes measured at the same ﬁxed beam from a vein at thedorsum manus of a 24-year-old healthy male. The M-mode
images were measured at rest (a), during avascularization(b), and after recirculation (c).
The vein measured in this study had a large diameter of
1 mm and a high blood shear rate, which aﬀected RBC
aggregation. Therefore, it was assumed that the RF echoes
scattered from nonaggregated RBCs were measured at rest.
Furthermore, we measured the change in scatterer diameterscaused by the decrease in the blood shear rate due toavascularization using a cuﬀ.
Figure 9(a) shows a M-mode image of the vein. The vein
was compressed so that the focal point corresponded to theposterior wall to obtain echoes reﬂected from the posteriorwall for normalization of power spectrum Ps ð f Þ of echoes

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1.5
normalized logarithmic
power spectrum

1.0 mm20 ms
anterior wall
lumen
windowwidth
posterior wall
window width

amplitude [V](b)external surface

0.5

rest (control)
during avascularization
recirculation

0.5
0
−0.5
4 µm
22 µm
8 µm

−1
−1.5
10

luminal surface

1

1

20
30
frequency [MHz]4050

Fig. 10. (Color online) Normalized logarithmic power spectra
log10 Ps ð f Þ=Pr ð f Þ and logarithmic theoretical power spectra
log10 QðkaÞ=a2 corresponding to the estimated scatterer diameters: at rest,
during avascularization, and after recirculation.

0
−0.5
−1

10.4

10.6

0

20

10.8
time [µs]

11

11.2

power spectrum [dB](c) −30
−35
−40
−45
−50
−55
−60
−65
−70
−75

40
60
frequency [MHz]

80

100

Fig. 9. (Color online) (a) M-mode image of the posterior wall of the veinat the dorsum manus of a 24-year-old male and focal point was placed on
the posterior wall. (b) RF echoes from posterior wall of the vein obtained bycompressing the vein. (c) Power spectra Pr ð f Þ of the ultrasound echoes
reﬂected from the posterior wall.

from RBCs. Figure 9(b) shows the RF echoes from posteriorwall of the vein. Figure 9(c) shows the averaged power
spectra Pr ð f Þ of echoes from the posterior wall of the vein at
the dorsum manus. In the present study, the window length
for applying fast Fourier transform was set at 0.256 s,
where it roughly corresponds to the duration of the echo
from the posterior wall. As shown in Fig. 9(c), the power
spectrum Pr ð f Þ from the posterior wall is obtained by echoesfrom the luminal surface of the posterior wall. On the other
hand, when echoes from the luminal and external surfaces
are included in the window for frequency analysis, the power
spectrum Pr ð f Þ shows dips due to the interference between
these echoes.
Figure 10 shows the normalized logarithmic power
spectra log10 Ps ð f Þ=Pr ð f Þ (solid line), and the logarithmic
theoretical power spectra log10 QðkaÞ=a2 (dashed line)
corresponding to the estimated scatterer diameters.
Figure 11 shows the transient change of averaged
estimated scatterer diameters with standard deviations
for three in vivo measurements with avascularization. The
scatterer diameters at rest and after recirculation were
estimated to be 4–8 m, which corresponded to the sizes ofnonaggregated RBCs. On the other hand, the scatterer

diameters during avascularization were estimated to beabout 12–22 m, which corresponded to the sizes ofaggregated RBCs and were greater than those at rest andafter recirculation. However, the standard deviations ofestimated scatterer diameters during avascularization arelarge because there would be various sizes of aggregated
RBCs. Scatterer sizes due to avascularization were varied
and blood ﬂow during avascularization was stopped byapplying pressure with a cuﬀ. In addition, RF echoes fromthe RBCs in the lumen could be diﬀerent with respect toeach measurement due to the displacement of the manus andblood ﬂow. Therefore, it is considered that the estimatedscatterer diameters in each measurement are widely diﬀerent
although the power spectrum was obtained by averaging
1000 power spectra of RF echoes.
5. Discussion and Conclusions

From the basic experiments using microspheres, it was
shown that the scatterer diameters could be estimated byminimizing the diﬀerence between the measured power
spectrum log10 Ps ð f Þ=Pr ð f Þ and the theoretical power
spectrum log10 QðkaÞ=a2 .
As shown in Figs. 5(b) and 7(b), the weighting functions
wð fk Þ are diﬀerent between basic experiments and in vivo
experiments. Figure 12(a) shows the M-mode images of RF
echoes and a example of the received RF echoes frommicrosphere (1) in Table I at three diﬀerent densities: (a)0.10, (b) 0.50, and (c) 1.00 g/l. As shown in Figs. 12(a) and12(b), the comet signs are observed in the three M-mode
images, which is considered to be caused by the multiple
reﬂection inside each microsphere.
Figure 13(a) shows the averaged power spectra Ps ð f Þ ofmicrosphere (1) in Table I obtained at three diﬀerent
densities of microspheres mixed with water: 1.00, 0.50,
and 0.10 g/l. Figure 13(b) shows the weighting function
wð fk Þ for each density of microsphere. As shown in
Fig. 13(a), the power spectrum Ps ð f Þ of echoes frommicrosphere (1) at the density of 1.00 g/l is inﬂuenced bydips, by contrast, the power spectra Ps ð f Þ of echoes frommicrosphere (1) at the density of 0.10 and 0.50 g/l are lessinﬂuenced by dips. As a result, dips in the power spectrum
are considered to be caused by the interference occurredfrom a number of microspheres. Therefore, the densityof microspheres mixed in the water should be further

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T. Fukushima et al.
1 mm

1 mm

1 mm

1 mm

scatterer diameter (2a) [µm]

80 s

480 s

260 s

rest
(control)duringavascularization

0200

recirculation

30
25
20
15
10
5
0

100

300
time [s]

400

500

600

Fig. 11. (Color online) Transient change of averaged estimated scatterer diameters with standard deviations during 10 min obtained by three in vivo

measurements. B-mode image in each phase of measurement is also shown.

20 ms

(a)
−30
power spectrum [dB]

1.5

1.0 mm(a)amplitude [V]

1

focus

0.5
0

−0.5
−1
−1.5

10.4

10.6

10.8
time [µs]

11

11.2

−40
−50
−60
−70

0.8

1.0 mm(b)

20 ms

amplitude [V]

0.6

focus

1.0 g/l
0.5 g/l
0.1 g/l

0

0.4

20

0.2

40
60
frequency [MHz]

80

0

(b)

−0.2

1
1.0 g/l
0.5 g/l
0.1 g/l

−0.6

10.6

10.8
time [µs]

11

11.2

0.8
0.6

amplitude [V]

1.0 mm
focus

10.4

20 ms

weighting function

−0.4

(c)

100

0.4
0.2
0
−0.2

0.8
0.6
0.4
0.2

−0.4
−0.6
−0.8

0
10.4

10.6

10.8

11

11.2

time [µs]Fig. 12. (Color online) M-mode images of RF echoes and an example of
the received RF echoes from microsphere (1) in Table I at three diﬀerent
densities: (a) 0.10, (b) 0.50, and (c) 1.00 g/l.

considered. On the other hand, as shown in Fig. 13(b), theweighting functions wð fk Þ show large values between 50 and
90 MHz regardless of the density of microsphere. Therefore,
the inﬂuence of multiple scattering are not a dominantreason on the diﬀerence between the weighting functions
wð fk Þ in basic experiments and in vivo experiments.
Figure 14 shows RF echoes scattered from microspheres(blue line) and from RBCs (red line) in the lumen. As shownin Fig. 14, the main reason for the diﬀerence of weighting

0

20

40
60
frequency [MHz]

80

100

Fig. 13. (Color online) (a) Power spectra Ps ð f Þ of the ultrasonic echoesfrom the microsphere (1) in Table I obtained at diﬀerent densities of
microspheres mixed with water. (b) Weighting functions wð fk Þ obtained
from MSCF among the ultrasound echoes scattered from microsphere (1) in
Table I for each density of microspheres.

functions wð fk Þ is considered to be the strong scattering of
microspheres because the MSCF was used as the weighting
function wð fk Þ and the SNR of the echoes, which isevaluated by the MSCF, obtained from microspheres arelarger than that of echoes from RBCs in the lumen of thevein. The diﬀerence of acoustic impedance between microspheres and RBCs should be further considered in the futurework.

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Jpn. J. Appl. Phys. 50 (2011) 07HF02

T. Fukushima et al.

0.8

amplitude [V]Acknowledgment

RBCs in the lumen
microsphere (1)0.6

We would like to thank Tomey Corporation for its
cooperation on the use of the diagnostic equipment.

0.4
0.2
0
−0.2

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spectra log10 Ps ð f Þ=Pr ð f Þ are strongly aﬀected by dips inmeasured power spectra Pr ð f Þ with interference obtained by
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# 2011 The Japan Society of Applied Physics