Journal of Medical Ultrasonics (2019) 46:3–14
https://doi.org/10.1007/s10396-018-0892-z

ORIGINAL ARTICLE

Ultrasound scattering by aggregated red blood cells in patientswith diabetes
Hiroki Sakaki1 · Mototaka Arakawa1,2 · Satoshi Yashiro3 · Yusuke Todate3 · Yasushi Ishigaki3 · Hiroshi Kanai1,2
Received: 20 March 2018 / Accepted: 5 July 2018 / Published online: 30 August 2018
© The Japan Society of Ultrasonics in Medicine 2018

Abstract
Purpose To develop methods for noninvasively and quantitatively measuring blood glucose levels.
Methods In the present study, we evaluated the degree of red blood cell (RBC) aggregation at a low shear rate robustly byintroducing two new parameters determined from changes in the scattering power spectrum of the echoes from the intravascular lumen before and after cessation of blood flow. We also considered the clinical significance of these parameters and thechange in sizes estimated by the conventional method by comparing them with the blood glucose level obtained just before
the ultrasonic measurements. We performed the measurements in one healthy subject and 11 diabetic patients.
Results A correlation was found between one of the proposed parameters and the blood glucose level. However, the p value
was not very high, and one of the reasons for the decline of the correlation will be that some factors other than blood glucose
also affect RBC aggregation.
Conclusion The proposed method has potential for clinical application after elucidation of the various factors affecting RBC
aggregation.
Keywords Ultrasound scattering · Red blood cells · Aggregation · Blood glucose levels

Introduction
According to the International Diabetes Federation, there
were 415 million people with diabetes worldwide in 2015,
i.e., 8.8% of the adult population. In Japan, diabetic patients
have gradually increased up to 7.2 million people. Diabetic
patients must measure their blood glucose levels with multiple skin punctures to achieve optimal blood glucose control,
resulting in a burden due to the invasiveness of the procedureand the high cost of monitoring strips. Several methods fornoninvasively measuring blood glucose levels have beendeveloped, such as measurement of the heat generated during oxidation of glucose in the blood [1, 2], or measurement* Hiroki Sakaki
hiroshi.kanai.e7@tohoku.ac.jp
1

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

2

Graduate School of Engineering, Tohoku University, Sendai,
Miyagi 980‑8579, Japan3

Department of Internal Medicine Division of Diabetes
and Metabolism, Iwate Medical University, Morioka,
Iwate 020‑8505, Japanof light absorption by glucose [3, 4]. However, devices basedon these techniques have yet to become clinically available.
On the other hand, medical ultrasound can be used repeatedly and noninvasively [5–13], and is already widely usedin clinical settings. To assess the condition of a patient’s
blood using medical ultrasound, a great deal of research has
been focused on the characteristics of backscattered echoesfrom red blood cells (RBCs) [14, 15]. In particular, RBC
aggregation, which is a reversible adhesion phenomenon, is
an important determinant of hematological properties [16,17]. An increase in blood viscoelasticity under a constantshear rate is reported to be primarily due to an increase in
RBC aggregation [18]. Moreover, blood viscosity has been
confirmed to increase when blood glucose levels (BG) arehigh [19], leading to measurable differences, especiallywhen the blood flow is at a low shear rate. Therefore, blood
glucose levels (BG) can be assumed to be correlated with
RBC aggregation. As a result, measuring RBC aggregation
at low shear rates may be useful for evaluating blood glucose
levels (BG).
With ultrasound imaging, though “smoke-like echoes”
are known to occur in the vascular lumen based on the
degree of RBC aggregation [20], this assessment is only

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qualitative. Therefore, development of a diagnostic indicator
to quantitatively evaluate RBC aggregation is still needed.
Patat et al. observed changes in the speed of sound andscatterer size during the process of blood coagulation within vitro measurements [21, 22]. Cloutier et al. estimated thesize of RBC aggregation using the structure factor and attenuation estimator [23]. However, these studies were directly
applied to blood collected invasively.
In our previous study, Fukushima et al. proposed amethod to estimate the size of RBC aggregation by fitting
the power spectrum of the scattered ultrasound wave fromthe intravascular lumen with theoretical scattering properties[24]. To eliminate the properties of the transfer function of
the ultrasonic probe, the scattered power spectrum from theintravascular lumen was normalized by the power spectrumof the RF signal reflected from the posterior wall of the veinat the same site. Kurokawa et al. found that the effectiveness of beam selection for calculating the reflected power
spectrum from the posterior wall of the vein significantly
improved the accuracy of the aggregate size estimation [25].
However, the size estimation was still not stable, which canbe explained by the fact that the difference in the propagation attenuation between the scattered wave from the intravascular lumen and the reflected wave from the posteriorwall of the vein is not negligible.
In the present study, therefore, the degree of RBC aggregation at a low shear rate was evaluated more robustly byintroducing a novel normalization method so that the difference in the propagation attenuation was removed, and newparameters were determined from changes in the scattering
power spectrum of the echoes from the intravascular lumen
before and after the cessation of blood flow. The present
study also considered the clinical significance of the estimated size and the parameters by comparing them with theblood glucose level (BG) measured just before the ultrasonicmeasurements.

Journal of Medical Ultrasonics (2019) 46:3–14

scattering property when the scatterer is irradiated by a plane
wave is given by [29]
∞
∑
]
Q(ka)
2n + 1 2 [ �=sin 𝛿n (ka) ,224𝜋an=0 (ka)(1)

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 𝛿n� (ka) is thederivative of the phase difference between the incident andscattered waves. The theoretical scattering property of eachsize of scatterer obtained from Eq. (1) is shown in Fig. 1.
The ultrasound scattering power strongly depends on frequency. The slope of the scattering power changes by thesize of the scatterer in a limited frequency range. Thus, thefrequency property of the ultrasonic scattering power |S(f )|2
in a certain frequency bandwidth can be approximated by(2)
where f is the frequency, C is the coefficient, and n is thefrequency dependence. The common logarithm of Eq. (2)is given by|S(f )|2 = C × f n ,log10 |S(f )|2 = n × log10 f + log10 C.

(3)

The frequency dependence n shows the slope of the logarithmic power spectrum against log10 f , and n is treatedas constant in a certain frequency bandwidth, as shown in
Fig. 1.
The frequency dependence n and the scattering power|S(f )|2 were calculated for the theoretical scattering property
in the frequency range of 27–45 MHz, as shown in Fig. 1. The
results are shown in Figs. 2 and 3, respectively. As the scatterer increases in size, the frequency dependence n becomes
weaker, and the scattering power increases. That is, both thefrequency dependence n and the intensity of the scattering
power depend on the target scatterer size. In the present study,

Materials and methods
Ultrasound backscattering
When the scattering source in a target tissue is much smaller
than the wavelength of the incident wave, Rayleigh scattering occurs, and the backscattered power is proportional to
the fourth power of the frequency [26, 27]. When the scatterer is much larger than the wavelength of an incident wave,
reflection occurs, and the backscattered power is independent of the frequency.
In the present study, a scatterer was modeled by assuming an infinite number of infinitesimal point sources on thesurface of a spherical scattering source [28]. The theoretical

13{}
Fig. 1  Theoretical power spectrum log10 Q(ka)∕4𝜋a2 with constantvalues for each scatterer diameter (2a)

Journal of Medical Ultrasonics (2019) 46:3–14

5

ultrasonic probe and the ultrasonic equipment, and H(f , d)depends on the positions irradiated by the ultrasonic probe.
These three components can be assumed to be constant when
the ultrasonic probe is kept in the same position over thecourse of the measurements. Therefore, they can be removed
by normalizing the power spectrum acquired under the samemeasurement conditions.

Extracting the scattering property by normalization
In the previous methods in our group [24, 25], PS (f , d) was
normalized by the reflected power spectrum Pr (f , d) from theposterior wall of the vein to extract the scattering property|S(f )|2 . This process is expressed by
Fig. 2  Theoretical frequency dependence n for scatterer diameter (2a)

(
) (
)
(
)
|2
|
|S(f )As f , d0 H f , d0 G(f )X(f )|Ps f , d0||
10 log10 () = 10 log10
(
) (
)
|
|2
Pr f , d0|R(f )Ar f , d0 H f , d0 G(f )X(f )|||≈ 10 log10

Fig. 3  Theoretical scattering power for scatterer diameter (2a)40-MHz ultrasonic waves (wavelength = 38.5 μm) were used totarget a wide range of particle sizes, from a single RBC (maximum width = 8 μm) to large RBC aggregates. From Figs. 1,
2, 3, the amplitude changes are larger for smaller scatterers at
27–45 MHz. Therefore, the sensitivity of size estimation forthe larger scatterers should be less than that for the smaller
scatterers.
However, the ultrasonic scattering power spectrum Ps (f , d)of the measured signal calculated by Eq. (4) includes four
frequency properties other than the scattering property S(f )exhibiting a frequency dependence particular to the scatterersize, as follows:

Ps (f , d) = |S(f )A(f , d)H(f , d)G(f )X(f )|2 ,(4)

where d is the depth, X(f ) is the frequency spectrum of
the input voltage applied to the transducer, G(f ) is the frequency response of the transmitting and receiving properties of the transducer, H(f , d) is the sound pressure property
for focus formation, and A(f , d) is the attenuation propertyof the propagation medium. X(f ) and G(f ) depends on the|S(f )|2,|R0 |2| |(5)where d0 is the focal( length
probes, the( ultrasonic) of the)amplitude spectra As f , d0 and Ar f , d(0 are)the attenuation()
properties in the measurements of Ps f , d0 and Pr f , d0 ,respectively, and |R(f )|2 is the reflection property from thewall of the vein. Assuming that R(f ) is independent of thefrequency ( n = 0), it was approximated to be constant R0.
Figure 4a, b show the schematic diagram of acquisitionof RF signals scattered( from) RBCs to obtain the scattered
power spectrum Ps f , d0 and that of RF signals reflectedfrom a flat posterior(wall )of the vein to obtain the reflected
power spectrum Pr f , d0 , respectively, in the previously
proposed method. By considering the three attenuation
properties—the attenuation property Aw (f , d) in water andultrasonic echo gel, the attenuation property At (f , d) in
hypodermal tissues, and the attenuation property( Ab)(f , d)in (blood—eachoftheattenuation
propertiesAs f , d0 and
(
(
)
)
)
Ar f , d0 in Ps f , d0 and Pr f , d0 of Eq. (5) can be divided
into the three components as follows:

(
)
(
)
(
)
log10 As f , d0 = log10 Aw f , d1 + log10 At f , d2()
+ log10 Ab f , d3 ,

(6)

(
)
(
)
(
)
log10 Ar f , d0 = log10 Aw f , d1 − d3 + log10 At f , d2()
+ log10 Ab f , 2d3 ,(7)where d1, d2 , and d3 are the propagation distances in water,
hypodermal tissue, and blood, respectively, as shown in
Fig. 4, and both equations satisfy the relationship13

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Journal of Medical Ultrasonics (2019) 46:3–14

(a)

(b)

Fig. 4  Schematic diagrams of acquisitions of RF signals from a RBCs and b a flat posterior wall of the vein

d0 = d1 + d2 + d3. The difference in the propagation distances in water and blood in Eqs. (6) and (7) comes fromsetting of the different targets at the center of the intravascular lumen or the posterior wall of the vein, respectively, att h e( fo)c a l l (e n g t )h d0 . I n t h e a p p r ox i m a t i o n
As f , d0 ≈ Ar f , d0 applied in Eq. (5), the following dif)|2| (ference 10 log10 |ΔA f , d0 | in those attenuation properties||
remains as an error in the strict sense as follows:)|2| (10 log10 |ΔA f , d0 |
|
|
)|2
)|2
| (
| (
= 10 log10 |As f , d0 | − 10 log10 |Ar f , d0 |
|
|
|
|
{
(
)
(
)
= 20 log10 Aw f , d1 + log10 Ab f , d3()()}
− log10 Aw f , d1 − d3 − log10 Ab f , 2d3
)}
(
)
(
{
= 20 log10 Aw f , d3 + log10 Ab f , − d3 .

)|2
| (10 log10 |ΔA f , d0 | ≈ − 423.9 × 10−18 × f 2 + 635.8||
× 10−11 × f 1.14 (dB),(10)
where Aw (f , d) = e−𝛼w × 2d and Ab (f , d) = e−𝛼b × 2d wereassumed.
Figure 5 shows the frequency characteristics of)|2| (10 log10 |ΔA f , d0 | of Eq. (10). Since the reflection prop||2||
erty |R0 | was assumed to be a constant as in Eq. (5) in theprevious method,{the( slope)/ n of( the)}normalized power
spectrum 10 log10 Ps f , d0 Pr f , d0 for log10 f was fitted to the theoretical scattering property. However, as)|2| (shown in Fig. 5, since the difference 10 log10 |ΔA f , d0 |
|
|

(8)

)|2
| (
By introducing 10 log10 |ΔA f , d0 | , Eq. (5) can be||
rewritten without approximation as follows:
10 log10()
Ps f , d0)|2|S(f )|2| (+ 10 log10 |ΔA f , d0 | .
() = 10 log10|||R0 |2
Pr f , d0
| |

(9)
Since
the
attenuation
coefficient
of
water
is
/
/
coef𝛼w f 2 = 24.4 × 10/−18 s2 mm [30], the attenuation/
ficient of blood is 𝛼b f 1.14 = 36.6 × 10−11 s1.14 mm [31],and d3 is 1.0 mm based on past experiments in our group,)|2| (10 log10 |ΔA f , d0 | of Eq. (8) can be approximated by
|
|

13

)|2
| (
Fig. 5  Frequency properties of 10 log10 |ΔA f , d0 |||

Journal of Medical Ultrasonics (2019) 46:3–14

still exhibits frequency dependence, a systematic error
occurs in the determination{ () of (the slope)} n of the power
spectrum 10 log10 Ps f , d0 ∕Pr f , d0 in Eq. (5), which
introduces an error in the estimated size.
To suppress the systematic error due to the path length difference, the present study proposes a new method for normalization using the scattered power spectra of two different
scatterer sizes as follows. Figure 6 shows the schematic viewof acquisitions of RF signals scattered from two different scatterers. The smaller scatterers in Fig. 6a and larger scatterers
in Fig. 6b correspond to RBCs before aggregation and RBC
aggregates, respectively. The two different scattering power
spectra can be obtained by acquiring RF signals scatteredfrom RBCs before and after the stop of the blood flow, which
suppresses the effect due to the difference in path length that
occurred in the previous method, and the propagation attenuation A(f , d) can be removed by the following normalization.
(
) (
)
(
)
|2
|
|Sava (f )As f , d0 H f , d0 G(f )X(f )|Psava f , d0||
10 log10() = 10 log10
(
) (
)
|
|2
Psrest f , d0
|Srest (f )As f , d0 H f , d0 G(f )X(f )||||S (f )|2
ava
| ,= 10 log10 |(11)|Srest (f )|2||()
where Psrest f , d0 is thepower spectrum from the( scattered)smaller scatterer, Psava f , d0 is that from the larger scatterer,
Srest (f ) is the spectrum of scattering property of the smaller
scatterer at rest, and Sava (f ) is that of the larger scatterer after
avascularization. Normalization in Eq. (11) extracts the(a)7change inproperties{the scattering} for two scatterer sizes as
/
2
2 |
|
|
|
10 log10 |Sava (f )| |Srest (f )| .
From Eq. (2), the scattering properties ||Srest (f )|| and|Sava (f )|2 can be expressed as||
2|Srest (f )|2 = Crest × f nrest ,|||Sava (f )|2 = Cava × f nava ,||where Crest and Cava are coefficients, and nrest and nava are
the frequency dependences for the smaller scatterer and thelarger scatterer, respectively. As shown in Fig. 1, these four
coefficients can be assumed to be constant in a certain frequency bandwidth.
()
The normalized power spectrum Psnorm f , d0 is definedby the ratio of the scattering power of the larger scatterer tothat of the smaller scatterer as follows:|S (f )|2()
ava|
Psnorm f , d0 = ||Srest (f )|2
|
|
=

Cava
× f nava − nrest ,
Crest

(12)

(
)
where the frequency dependence in Psnorm f , d0 expresses
the change nava − nrest in the frequency dependence of thelarger scatterer from that of the smaller scatterer.
We introduce the following two new parameters, 𝜌 andΔn , for evaluation of the scattering power ratio(b)Fig. 6  Schematic diagrams of acquisitions of RF signals from the a smaller and b larger scatterers

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Journal of Medical Ultrasonics (2019) 46:3–14/
2|S (f )|2 |S (f )| and the change nava − nrest in the fre| ava | | rest |Basic experiments using microspheres

quency dependences, respectively. First, the parameter 𝜌concerned with the scattering power ratio is expressed by)][(
𝜌 = E 10 log10 Psnorm f , d0 ,(13)
f ≤f ≤f

Ultrasonic diagnostic equipment (UD-8000; Tomey, Japan)
with a mechanical scan probe operating at the central frequency of 40 MHz and a focal length of 9 mm was used.
The number of beams was 113. The beams were in the same
direction, and B-mode images were obtained from all the
beams. The RF echoes were acquired at a sampling frequency of 240 MHz, and their power spectra were obtainedby applying the Fourier transform with a Hanning windowof 0.15 µs at three positions along the depth direction foreach beam. The central window was set to the beam focal
depth, and the remaining windows were set to the depth
shifted up or down by 0.075 μs from the focal depth. The
mean scattered power spectrum for each frame was obtainedby averaging the power spectra of 339 signals detected fromall 113 beams.
Microspheres (Polyamide Seeding Particles; Dantec Dynamics, Denmark) with diameters of 5 and 20 µm
were used for simulating RBCs before aggregation and
RBC aggregates, respectively. The size distributions were
1–10 µm for 5-µm particles and 5–35 µm for 20-µm particles. The shape was not spherical but round. The number density was 6 × 103 and 9 × 101 mm−3 for 5- and 20-µm
particles, respectively. The single RBC has a diameter of
8 µm. The concentration of the aqueous solution of the
microspheres was 3.0 g/l. Before and after RBC aggregation, there should be no change in the weight concentrationof the RBCs. Therefore, we made the weight concentrationof microspheres for 5-µm and that of 20-µm particles thesame in the experiment. Each aqueous solution containing microspheres with different diameters was prepared ina beaker. The surface of the ultrasonic probe was inserted
into the solution in a stationary state. To disperse the microspheres, polyoxyethylene octylphenyl ether was used as thesurfactant.
Nineteen frames of RF echoes were acquired every 5 s.
To maintain the measurement conditions, the Hanning window was set at the same depth during the acquisition of the
19 frames. The scattering power ratio 𝜌 and the change(in the)Δn were calculated from Psrest f , d0
frequency( dependences)
and Psava f , d0 , which were obtained by averaging the power
spectra of the 19 frames during the measurement for the
microspheres of 5 and 20 μm, respectively.

12

where f1 and f2 were determined by considering the bandwidth of the ultrasonic probe. From Eq. (13), the scattering
power ratio 𝜌 is calculated by averaging the power of thenormalized power spectrum within the bandwidth.
Next, the parameter Δn concerned with the change inthe frequency dependences is expressed by(14)
which shows the slope of the logarithmic normalized power
spectrum within the probe bandwidth in the following
equation:
)
(
(
)
Cava
log10 Psnorm f , d0 = Δn × log10 f + log10, (15)
Crest

Δn = nava − nrest ,where the frequency bandwidth in the present study was set
at 27–45 MHz.
()
Figure 7 shows 10 log10 Psnorm f , d0 calculated using
Eq. (12), when the sizes of the smaller and larger scatterers are 5 and 20 μm, respectively, where the theoretical scattering property for each scatterer was calculated
by Eq. (1). The average of the normalized power corresponds to 𝜌 , and 1/10 of the slope of the normalized
power spectrum corresponds to Δn . As shown in Fig. 7,
Δn can be assumed to be almost constant in the bandwidth(27–45 MHz).

In vivo experiments()
Fig. 7  10 log10 Psnorm f , d0 in the case that sizes of the smaller andlarger scatterers are 5 and 20 µm

13

We performed in vivo experiments on human dorsal handveins. RBC aggregation tends to occur when the blood shear
rate becomes low [32]. Therefore, we measured ultrasonic echoes from RBCs with and without blood flow. The blood flow
was almost stopped using the application of about 250 mmHg

Journal of Medical Ultrasonics (2019) 46:3–14

9

of pressure using a cuff on the upper arm, and the condition
was confirmed on the B-mode image.
The measurement procedure was as follows. First, the posterior wall of the vein was set as the focus of the ultrasonicprobe, and RF echoes from the lumen-intima interface( were)acquired. Then, the reflected power spectrum Pr f , d0 of
Eq. (5) was calculated from the acquired RF echoes, and it
was used for normalization by the previous method. Then, thelumen of the vein was set as the focus, and the RF echoes fromthe RBCs were acquired while the subject was at rest for 1 min
and under avascularization conditions for 2 min. A total of
19 frames of RF echoes were acquired every
10() s. The power
spectrum of the smaller scatterer, Psrest f , d0 , was obtainedby averaging the power spectra of the first seven frames
at()
rest. The power spectrum of the larger scatterer, Psava f , d0 ,was obtained by averaging the power spectra of the six framesacquired during the latter half of the avascularization period.
Therefore, the scattering power ratio 𝜌 of Eq. (13) and thechange in the frequency dependences Δn of Eq. (14) wereobtained.
As a comparison, each scatterer size 2a was estimated basedon the previously developed{ ( method)} [25] from the scatteredaveraged power spectra Ps f , d0 obtained for the rest andavascularization phases. Then, the increase Δ(2a) in the average estimated size from the rest phase to the avascularization
phase was estimated.
Ultrasonic measurements were repeatedly performed in one
healthy subject under various conditions, including the fasting or post-prandial state. Then, the three parameters 𝜌, Δn,and Δ(2a) described above were obtained. Just before eachultrasonic measurement, the blood glucose level (BG) was
measured using a blood glucose measuring device (FreeStyle
Freedom ­Lite®; NIPRO, Japan). The fact that the subject was
healthy was judged based on not satisfying Diabetes Evaluation Criteria reported by the World Health Organization in2006 [33].
Ultrasonic measurements were also performed in 11 diabetic patients. For each analyzed subject, the plasma layer wasobserved in the uppermost intravascular lumen during the latter half of the avascularization period. This plasma layer isthought to form as a result of the RBC aggregation in the central region of the lumen, which depletes the concentration in
the uppermost intravascular lumen. The blood glucose levels(BG) were examined just before the ultrasonic measurement.
We compared the parameters 𝜌, Δn, and Δ(2a) with theblood glucose level (BG) for each measurement. The value ofthe correlation was evaluated by the coefficient of determination R2 of the straight-line fit, defined by

Results and discussion
Basic experiments using microspheres
Theoretical values of the scattering power ratio 𝜌 and thechange in the frequency dependences Δn for the sizes of 5
and 20 μm were calculated as 16.7 dB and − 2.60, respectively, from Fig. 1. On the other hand, those were measured
for microspheres of 5 and 20 μm as 16.9 dB and − 2.30,
respectively. While 𝜌 almost corresponded to the theoreticalvalue, Δn was slightly different from the theoretical one. The
robustness of each parameter against the influence of noise
was considered as follows.
The acquired RF signals include noise components otherthan the signal components. By introducing the frequency
property Ns (f ) of noise components, the scattered power
spectrum of Eq. (4) can be replaced by Ps + N (f , d) including
noise components as
2

Ps + N (f , d) = ||S(f )A(f , d)H(f , d)G(f )X(f ) + Ns (f )|| . (17)
By assuming that there is no correlation between the signal component and noise components,(18)
where PN (f ) is the power spectrum of noise components.
Figure 8 ( compares
the experimental spectrum)
10 log10 Psnorm f , d0 (dB) from the theoretical one calculated
from Eq. (1). The scattering( power) ratio 𝜌 can be obtainedby averaging 10 log10 Psnorm f , d0 in the bandwidth. Figure 9

Ps + N (f , d) = Ps (f , d) + PN (f ),∑ �2

R ≡ 1−� ��2yi − f xi
�2 ,
∑ �
y
−
y
̄
i
i

( )
where yi is measurement data, f xi is a linear regression
model, and ȳ is the averaged value of yi.

i

(16)

(
)
Fig. 8  Comparison between the experimental 10 log10 Psnorm f , d0 andthe theoretical one

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Journal of Medical Ultrasonics (2019) 46:3–14

{
(
/
(
))
(
/
(
))}
10 log10 1 + PN Psava f , d0 − log10 1 + PN Psrest f , d0()
Fig. 9  Comparison between the experimental log10 Psnorm f , d0 andthe theoretical one, and the approximate theoretical straight line forcalculating Δn()
compares the experimental spectrum log10 Psnorm f , d0 fromthe theoretical one calculated from Eq. (1), and the straightline for calculating Δn is shown.
As shown in Figs. 8 and 9, at the frequency close
to the outside of the frequency bandwidth (especiallyaround 27 MHz),the() power of the experimental spectrum
10 log10 Psnorm f , d0 was lower than the theoretical value.
By assuming that the power of the experimental spectrum
includes noise components PN (f ) and they are constant as
PN , it is expressed by)(
10 log10 Psnorm + N f , d0()
Psava f , d0 + PN
= 10 log10()
Psrest f , d0 + PN{
= 10 log10()
Psava f , d0 1 +({− 10 log10

PN()
Psava f , d0(()
Psrest f , d0 1 +

(

)

PN
(
)
Psrest f , d0{(

= 10 log10 Psnorm f , d0 + 10

log10

(

)}

− log10PN
1+()
Psrest f , d0

)}

.

)}

PN
1+
(
)
Psava f , d0

)

(19)

Thus, the experimental value including the noise
component has the additive power difference of

13

compared with the theoretical value without noise components. Therefore, the degree of such( influenceis roughly())
dominated by the ratio of PN(to Psava
and
P
f
,
d
0
( srest)) f , d0 .
On the other hand, when Psava f , d0 and Psrest f , d0 are sufficiently larger than PN , the influence of noise components
is negligible.
as shown in Fig. 3, the scattering( However,
)
power
of
the
smaller scatterer is smaller than
P
f
,
d
s
0
rest
(
)
Psava f , d0 of the larger scatterer, especially at a lower frequency. Furthermore, − 6 dB bandwidth in the experiment()
in the present study was 27–45 MHz. Therefore, Psrest f , d0
around 27 MHz is assumed to be small, and the influenceof the noise of the last term of Eq. (19) cannot be canceled,
and then the (normalized
power of Eq. (19) decreases from)
10 log10 Psnorm f , d0 of Eq. (11), which introduces error in
the estimation of the parameters of 𝜌 and Δn.
As shown in Fig. 8, since the scattering power ratio 𝜌
was calculated by averaging the normalized power within
the frequency bandwidth, errors generated around 27 MHz
can be reduced. On the other hand, since the change in thefrequency dependences Δn was calculated by approximating the slope of the normalized power within the frequency
bandwidth as shown in Fig. 9, Δn was unfortunately affectedby errors around 27 MHz. Therefore, the scattering power
ratio 𝜌 is more robust than Δn.

In vivo measurements
The parameters 𝜌 , Δn , and Δ(2a) were compared with theblood glucose level (BG) for each measurement in one
healthy subject under various conditions, including thefasting or post-prandial state, as shown in Fig. 10. A blood
glucose level higher than 100 mg/dl corresponds to the datameasured after meals. From Fig. 10a, the highest correlation was obtained for the relationship between the ratio 𝜌and (BG).
Next, for 11 diabetic patients, the parameters 𝜌, Δn, andΔ(2a) were compared with the blood glucose level (BG), as
shown in Fig. 11. From Fig. 11a, the highest correlation was
also found between the ratio 𝜌 and (BG).
The p value of the scattering power ratio 𝜌 and the blood
glucose level was 0.03 (∗ p < 0.05) for the healthy subject,
and that for the diabetic patients was 0.19 ( p > 0.05). Thus,
clinical significance was somewhat shown in the one healthy
subject and not shown in the diabetic patients.
Therefore, the following additional experiments were
performed in the same healthy subject three times, which
we refer to as Ex. A, B, and C. In each experiment, the ultrasonic measurements and blood glucose level (BG) measurements were performed after fasting for 12 h. Both measurements were performed five times at intervals of about
30 min. Table 1 shows the blood glucose level (BG) and thescattering power ratio 𝜌 for each experiment as a function

Journal of Medical Ultrasonics (2019) 46:3–14

11Fig. 10  The blood glucose level and three analysis parameters, which
are a 𝜌, b Δn, and c Δ(2a), in a healthy subject. Closed circles: measurement data, solid line: approximated line

Fig. 11  The blood glucose level and three analysis parameters, which
are a 𝜌, b Δn, and c Δ(2a), in 11 diabetic patients. Closed circles:
measurement data, solid line: approximated lineof time from the ingestion of glucose. Glucose (18 g) was
ingested just before the second measurement in Ex. A, andjust before the third measurement in Ex. B and C. With the
exception of Ex. C, both the blood glucose level (BG) andthe scattering power ratio 𝜌 remarkedly increased just afteringestion of glucose. On the other hand, the blood glucose
level (BG) further increased despite the scattering power
ratio 𝜌 decreasing 30 min after ingestion of glucose.

We discuss this transitionas(( shows) follows: Fig. 12)
the power of 10 log10 Psrest f , d0 and 10 log10 Psava f , d0 of
Eq. (11) against the time from ingestion of glucose in eachexperiment. (From)Fig. 12, for all experiments, the power of
10 log10 Psrest f , d0 decreased immediately after ingestion of
glucose.
Figure 13a, b show the B-mode image during the resting
period in measurements 2 and 3, respectively, in Ex. B. The
brightness in the intravascular lumen became clearly low

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Journal of Medical Ultrasonics (2019) 46:3–14

Table 1  Blood glucose level and scattering power ratio 𝜌 of eachexperiment as a function of time from ingestion of glucose
In vivo measurement times
Experiment A
1
2
3
4
Experiment B
1
2
3
4
5
Experiment C
1
2
3
4
5

Time from ingestion Bloodof glucose (min)glucose(mg/dl)Scattering
power ratio 𝜌
(dB)

− 35
+5
+ 33
+ 77

93
119
160
85

5.6
11.4
8.5
8.6

− 35
− 27
+ 10
+ 34
+ 68

93
93
122
142
76

9.1
6.4
12.9
10.3
9.7

− 79
− 37
+ 14
+ 39
+ 67

89
89
137
124
77

10.6
8.6
7.7
4.8
0.8

in measurement 3 as compared with measurement 2. Thus,
RBCs did not aggregate in the rest period after ingestion of
glucose. Although the cause is unknown, some factors otherthan the blood glucose level (BG) also influenced the aggregation of RBCs. Thus, the correlation between the scattering
power ratio 𝜌 and the blood glucose level (BG) decreased.
We will continue to investigate the factors.

Conclusion
The present study proposed a new normalization method
for avoiding the effect of path length difference to accurately evaluate the degree of RBC aggregation by introducing new parameters 𝜌 and Δn . The ultrasound-based
method proposed in the present study is noninvasive andinexpensive compared with other instruments for measuring blood glucose levels (BG). There is a possibility
that some factors other than blood glucose affected the
RBC aggregation, and a few problems with the proposed
method still remain, but the method has the potential tononinvasively measure blood glucose levels (BG). In the
proposed method, it is necessary to perform measurements
during flow and under stationary conditions. However, theDoppler effect does not affect the measurement, because of

13()
Fig. 12  The maximum() power of 10 log10 Psrest f , d0 (solid circles)
and 10 log10 Psava f , d0 (open circles) against the time from ingestionof glucose in Experiments a A, b B, and c C

the difference in the ultrasonic velocity in blood and bloodflow velocity. Otherwise, the difference in propagation
loss caused by the different scattering under the different

Journal of Medical Ultrasonics (2019) 46:3–14

(a)

13

1 mm

1 mm

skin
lumen

(b)

1 mm

1 mm

skin
lumen

Fig. 13  B-mode image of the resting period in a measurement 2 andb measurement 3

conditions would affect the measurement. We will discuss
this effect in a future paper.
Acknowledgements This work was partly supported by MEXT/JSPS
KAKENHI through Grant No. 16K14272.

Compliance with ethical standards
This study was approved by the Institutional Review Board of Iwate
Medical University (Approval Number: H26-79). Written informed
consent was obtained from study participants.
Conflict of interest The authors have no conflicts of interest with regard to the presented research.

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