Journal of Medical Ultrasonics (2022) 49:529–543
https://doi.org/10.1007/s10396-022-01229-z

ORIGINAL ARTICLE–PHYSICS & ENGINEERING

Evaluation of local changes in radio‑frequency signal waveformand brightness caused by vessel dilatation for ascertaining reliabilityof elasticity estimation inside heterogeneous plaque: a preliminary
study
Yuta Haji1 · Shohei Mori2· Mototaka Arakawa1,2 · Toshio Yamagishi3 · Hiroshi Kanai1,2

Received: 4 February 2022 / Accepted: 9 May 2022 / Published online: 16 July 2022
© The Author(s), under exclusive licence to The Japan Society of Ultrasonics in Medicine 2022

Abstract
Purpose To diagnose plaque characteristics, we previously developed an ultrasonic method to estimate the local elastic
modulus from the ratio of the pulse pressure to the strain of the arterial wall due to dilatation in systole by transcutaneously
measuring the minute thinning in thickness during one cardiac cycle. For plaques, however, some target regions became
thicker as the vessel dilates, resulting in false elasticity. Therefore, a method to identify a reliable target for the elastic modulus estimation is indispensable. As a candidate for an identification index of plaques that become thicker during one cardiac
cycle, the correlation of the radio-frequency (RF) signals remains high and it is not sufficient to obtain the elasticity. In thisstudy, we thoroughly observed the target with a high correlation but positive strain in the plaque and characterized it by theproperty of the surrounding area.
Methods For the plaque formed in the right carotid sinus of a patient with hyperlipidemia and the wall of the right common carotid artery of a young healthy male, (1) the correlation value as the similarity between the RF signals, (2) change inbrightness obtained from the log-compressed envelope signals, and (3) strain obtained between the time of the R-wave andthat of the maximum vessel dilatation were observed to characterize the region in the plaque.
Results In the plaque, it was found that the region with high correlation and positive strain and its surrounding area could
be classified into one of the three typical patterns.
Conclusion As a preliminary study, this study provides a clue to assert the reliability of elasticity estimates for a region withhigh correlation and positive strain in the plaque based on measurable properties.
Keywords Atherosclerosis · Plaque · Carotid artery · Elasticity · Strain

Introduction
One of the main causes of cerebral and myocardial infarctions is the rupture of vulnerable plaques in atherosclerosis[1, 2]. As atherosclerosis progresses, plaques, which consistof lipid components, form on the vessel walls. The flow of* Shohei Mori
mori@tohoku.ac.jp
1

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

2

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

Department of Internal Medicine, Tohoku Kosai Hospital,
Sendai 980‑0803, Japanthe lipid components into the blood following the ruptureof the plaque introduces serious illnesses, such as cerebral
or myocardial infarctions. Thus, plaques with a high risk ofrupture are rich in soft tissues, such as lipids and blood clots,
whereas stable plaques with a low risk of rupture consist of
hard tissues, such as fibrotic tissues. Therefore, a noninvasive evaluation of the internal tissue characteristics of theplaque helps to diagnose the risk of plaque rupture.
Computed tomography (CT) [3], magnetic resonanceimaging (MRI), and intravascular ultrasound (IVUS) [4,5] are used to diagnose atherosclerosis. However, CT uses
X-ray radiation, CT and MRI require large-scale equipment, and IVUS is invasive; therefore, the use for repeatable follow-ups of plaque in clinics is difficult. The main
noninvasive diagnostic method for atherosclerosis is the13Vol.:(0123456789)

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measurement of intima-media thickness (IMT) using ultrasound [6]. This method mainly measures the shape of thearterial wall and the size of the plaque; however, it is insufficient to assess the risk of plaque rupture.
One approach to diagnosing the tissue characteristics ofthe vessel wall is to measure the stiffness or elasticity ofthe vessel wall. The vascular compliance [7, 8], pulse wave
velocity (PWV) [9, 10], stiffness parameters [11, 12], andelasticity measured from the change in the arterial diameter [13] have been used as indices of stiffness. However,these methods measure the spatially averaged stiffness ofthe entire vessel wall in the measurement target. Plaquecomprises soft tissues, such as lipids, and hard tissues,
such as fibrotic tissues, and its structure is heterogeneous.
To determine the tissue characteristics of the plaque, it isnecessary to characterize the local stiffness rather than
the spatially averaged properties of the entire vessel wall.
Our group has proposed a method to estimate the twodimensional distribution of the local elastic modulus of
the arterial wall by measuring its regional minute thinning deformation caused under pulse pressure using an
ultrasound system with a transcutaneous linear array probe[14–16]. This method enables the evaluation of local characteristics and composition inside the plaque, which has aheterogeneous structure [17–20]. This method was applied
to clinical studies of patients with atherosclerosis [21, 22],
lifestyle-related diseases [23], obese subjects [24], andpatients with type 2 diabetes [25–27].
In this method, the elastic modulus is obtained using theproperty where the vessel wall becomes slightly thinnerwith vessel dilatation during one cardiac cycle based on
the volume preservation of the wall as follows: using thecorrelation, the decrease in the thickness, Δh(n) , between
the two points set along an ultrasonic beam in the arterial
wall is measured during one cardiac cycle. Then, the maximum change in thickness, |Δh|max , of Δh(n) caused by thepulse pressure Δp is obtained. By dividing |Δh|max by theoriginal thickness h0 before the vessel dilatation, the strain
ε along the beam direction is obtained by assuming that
there are no displacements in the lateral and/or elevational
directions. The elastic modulus Eθ along the circumferential direction θ is estimated by dividing the pulse pressure
Δp by the strain ε.
For plaque, however, the strain is sometimes measured
as positive in a local region, i.e., regional thickening occurs
even though the entire vessel is dilated. Lipid components
in the plaque deform fluidly during vessel dilatation, i.e.,
the property of regional mobility. This property may cause
minute local displacement in the lateral and/or elevational
directions within the plaque. This mobility is related to theprogression of atherosclerosis, and plaques with high mobility show the “jellyfish sign,” which is a high-risk factor forstroke [28].

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Journal of Medical Ultrasonics (2022) 49:529–543

If a target within the plaque is mobile, it may move out
from the measured cross-sectional plane or another target
may enter into the measured cross-sectional plane with vessel dilatation. These movements disturb the correct evaluation of the elasticity Eθ based on the measured maximum
change in thickness, |Δh|max , along the ultrasonic beamcaused by the pulse pressure Δp, and the resultant apparent
strain ε may be positive. Thus, the obtained strain ε shouldbe evaluated by some other indexes. One of the possible
indexes is the correlation of the RF signals. However, sincethese movements are minute, i.e., several tenth micrometers,
the correlation of the RF signals remains high even if theresultant strain ε is positive.
In this study, to identify the targets where the measured
strain ε becomes unreliable, which is not appropriate forthe calculation of the elastic modulus Eθ , we thoroughly
observed the local change in RF signals using correlation
R and the local change in brightness, ΔB, inside the plaqueduring vessel dilatation, where the brightness is obtained
from the log-compressed enveloped RF signal to widen
the dynamic range. These evaluations of R and ΔB wereobtained from the time of the R-wave of the electrocardiogram (ECG), just before the beginning of the vessel dilatation, to the time of maximum vessel dilatation. The strain ε,correlation R , and change in brightness ΔB between these
two times were observed for each target for plaques, andthese were compared with ε, R, and ΔB for the healthy common carotid artery (CCA).

Principles and methods
Measurement of local change in thickness and strain][
Let us consider a small target d0 − w2 , d0 + w2 around thedepth d0 with width w along the ultrasonic beam in the arterial posterior wall at a time of the R-wave of ECG, as shownin Fig. 1(1). As shown in Fig. 1(2), due to vessel dilatation,
the target moves deeper from d0 to dn at the n th frame andthe target becomes thinner. Let us define the 0th frame by
the time of the R-wave of ECG, which is just before thebeginning of the vessel dilatation.
Let us describe its thickness at the n th frame by hd0 (n).
The thickness at a time of R-wave (0th frame) is set byw (385 μ m in this study), i.e., hd0 (0) = w, and the local axial[displacements] of both edges of the target regiond0 − w2 , d0 + w2 are tracked using RF data. As shown in
Fig. 1(2), let us denote these displaced depths by))((
zd0 − w (n) + d0 − w2 and zd0 + w (n) + d0 + w2 , where the
2
2
)
)
(
(
w
second terms d0 − 2 and d0 + w2 show the initial depths
at the 0th frame, where zd0 − w (0) = zd0 + w (0) ≡ 0. The thick22

Journal of Medical Ultrasonics (2022) 49:529–543

531

Fig. 1  (1) An illustration of a B-mode image around a plaque in thevessel wall and a target at the center depth d0 with width w along theultrasonic beam inside the wall at a time of R-wave (0th frame). (2)The vessel wall dilates and the wall becomes thin during one cardiac cycle. a B-mode image of the CCA of a healthy subject andthe analyzed region between the two red lines, and beam position
for analysis (white line). Along with the lateral position, b correlation Rndmax (d0 ) between RF signals at a time of R-wave and that of the( )maximum dilatation, c strain 𝜀 d0 at a time of the maximum dilatation of the vessel. For these data( alongd( )) with 47 lateral positions,distribution of correlation {Rndmax d0 } and brightness {B0 d0 }, and( )( )e distribution of {Rndmax d0 } and strain {𝜀 d0 }. During one cardiac
cycle for the data along the white line of a, f ECG, g correlation
Rn (d0 ) between RF signals at the time of R-wave and that at the nthframe, h displacement in the beam direction, zd0 (n), i change in thickness, Δhd0 (n), and j displacement in the lateral direction, x(n)ness hd0 (n) of the target region at the nth frame is obtainedby the difference between these displaced depths as
)} {
)}
{
(
(
w
w
− zd0 − w (n) + d0 −
hd0 (n) = zd0 + w (n) + d0 +
2
2
2
2
w
w
= zd0 + (n) − zd0 − (n) + w, [m]( ) Δhd0 (ndmax ) zd0 + w2 (ndmax )−zd0 − w2 (ndmax )𝜀 d0 =
=
.
w
w

2

2

(1)

where these displacements, zd0 − w (n) and zd0 + w (n) are meas2
2
ured using the phased tracking method [29]. Moreover, thechange in thickness, Δhd0 (n), of the target region is given by

Δhd0 (n) = hd0 (n) − w= zd0 + w (n) − zd0 − w (n).[m]
2

(2)

2

As shown in Fig. 1(2), let ndmax be the frame of the time of
maximum vessel dilatation, and let us assume that each target
in the vessel wall along the ultrasonic beam has the( minimum)
thickness at the ndmax-th frame. The maximum strain 𝜀 d0 caused
during one cardiac cycle around the target depth d0 is obtained by(3)

Calculation of local elasticity of arterial wall( )The local elastic modulus Eθ d0 in the circumferential
direction for the target set around the center depth d0 withwidth w along the ultrasonic beam inside the wall is obtained
as follows from the ratio of the pulse pressure( Δp) measured
with a sphygmomanometer to the strain 𝜀 d0 measured
around the depth d . The derivation of the following equationand the underlying assumptions are described in Appendix:() w Δp( )r0 +d0 − w2 −dw
h0, [Pa]
Eθ d0 = 43 21 +w
−𝜀(d0 )

(4)

where h0 ≥ w is the initial thickness of the vessel wall at thetime of R-wave, r0 is the initial inner radius of the vessel at
the time of R-wave, and dw < d0 is the depth of the interface

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Fig. 1  (continued)

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Journal of Medical Ultrasonics (2022) 49:529–543

Journal of Medical Ultrasonics (2022) 49:529–543

533

between the lumen and the inner surface of the vessel wall
[15, 30,(31],) as shown in Fig. 1(1). From this definition, thestrain𝜀d( ) 0 should be negative to obtain the elastic modulusEθ d0 .

Evaluation of local change in RF signal waveform
due to vessel dilatation“the correlation being high” is not sufficient to exclude thesetargets from the calculation of the elastic modulus.

Evaluation of local change in brightness due
to vessel dilatation
When local displacements in the lateral and/or elevational
directions occur inside the plaque, the brightness values
and regional brightness patterns on the B-mode image may
change. Therefore, for the same target around the depth d0
set at the 0th frame along( ) an ultrasonic beam inside theplaque, the change ΔBn d0 in brightness from the 0th frameto the nth frame is given by

For each frame, an RF signal is acquired along each( ultra)
sonic beam. As shown in Fig. 1(1), let us denote sn dn as
the RF signal of the nth frame around the object, the depthof which is dn at the nth frame.
The local change in the RF signal with vessel dilatation
Rn (d0 )is evaluated using the normalized( cross-correlation)
between the local RF(signal
at
the
0th
frame
and
s
d
0 0
)
the local RF signal sn dn at the n th frame. To obtain theRn (d0 ) between local waveforms in the same target inside
the plaque, the center position dn of the correlation windowat the nth frame should be maintained at the same positionin the depth direction inside the plaque at the 0th frame.
This is realized by moving the correlation window with dnalong with the local displaced depth zd0 (n) + d0 for the point
set at a depth d0 of the 0th frame, which is measured by thephased tracking method [29], where dn = zd0 (n) + d0 . Thus,
the normalized cross-correlation Rn (d0 ) between s0 (d0 ) andsn (dn ) is given by

where Bn (d) [dB] is the brightness with a value of the logcompressed enveloped signal at depth d of the n th frame toincrease the dynamic range. ( )In addition to the strain 𝜀 d0 of Eq. (3), the correlation( R) n (d0 ) of Eq. (5) and the change in brightness
ΔBn d0 of Eq. (6) were evaluated between the time of
the R-wave and thendmax of the maximum( time)( )vessel
dilatation, i.e., 𝜀 d0 , Rndmax (d0 ) , and ΔBndmax d0 were
evaluated below.

N � �
�� �
�
�
� �
�
∑
1
Rn d0 = 𝜎 1𝜎 2N+1
s0 d0 + i ⋅ 𝛿z − s0 sn dn + i ⋅ 𝛿z − sn ,Measurement of lateral displacement x(n)

0 n

i=−N

(5)

where the width of the correlation window is (2N + 1)
points, sn and 𝜎n are the mean and standard deviation ofsn (dn ) in the correlation window at the n th frame, respectively, and 𝛿z [m] is the spatial interval for sampling the RF
signal in the depth direction z , where 𝛿z = 19.25 µm in thispaper. The value of N is determined so that the width of(2N + 1) points ×𝛿z equals w = 385 µm.
||
To deal with |zd0 (n)| of minute displacement much less||than 𝛿z , the correlation Rn (d0 ) of Eq. (5) was interpolated at
the sampling interval by a factor M based on the reconstructed interpolation method [32] by convoluting the sincfunction. For the lateral direction, the sampling interval was
equal to the beam interval 𝛿x determined by the ultrasonicprobe. When the lateral and/or elevational displacements
regionally occur in the internal tissues of the plaque due tovessel dilatation, the RF signal may change, and then Rn (d0 )decreases; that is, the high correlation indicates the absenceof the effects due to the lateral and/or elevational
displacements.
For the actual data, however, some targets become thickeven when the vessel wall is dilated, as shown below. Thus,

N
� �
�
�
��
∑
� �
1
ΔBn d0 = 2N+1
�Bn dn + i ⋅ 𝛿z − B0 d0 + i ⋅ 𝛿z �, [dB]
�
�
i=−N
(6)

During one cardiac cycle, lateral displacement of the carotid
artery occurs because of the force exerted by contraction of theheart. To detect the effect of lateral displacement on the strain
measurement, the lateral displacement x(n) of the entire vessel
wall was measured using the block matching method [33, 34],
by neglecting the regional difference in the lateral displacement.
For calculating the two-dimensional (2D) normalized crosscorrelation function of the enveloped RF signals, the size of theregion R was ±0.54 mm in the depth direction by ±1.05 mm in
the lateral direction for the plaque and ±0.08 mm in the depth
direction by ±1.05 mm in the lateral direction for the CCA. Since
the width of the 47 ultrasonic( )beams in the lateral direction( ) wasemployed for obtaining ε d0 , Rndmax (d0 ), and ΔBndmax d0 , theregion R was set almost in the center of the lateral direction with
47 beams at the 0th frame. The RF signal contains the amplitude
and phase components. Even if an object moves along the lateral
direction by keeping its depth, the phase values of the RF signals
between the different beam positions randomly change because
there is variance in the speed of sound for the soft tissue from theultrasonic probe to the anterior wall. Thus, the 2D normalized
cross-correlation function is obtained from the enveloped RF
signal to ignore the phase component.

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The employed maximum lag ( 𝜏z , 𝜏x ) in calculating the
2D normalized cross-correlation function was ±0.075 mm
in the depth direction and ±0.75 mm in the lateral direction
for the plaque and ±0.055 mm in the depth and ±0.75 mm
in the lateral direction for the CCA. The data used for the
calculation of the cross-correlation function were restrictedin the intima-media complex (IMC) for the healthy CCA
or inside the plaque. The resultant 2D cross-correlation
function is interpolated using a reconstructive interpolation
method [32].

Experimental method
A linear array probe with a center frequency of 7.5 MHz
and 192 elements was connected to a diagnostic ultrasoundsystem (SSD-6500; Aloka, Japan). The focus was fixedat 18.7 mm from the probe. The sampling frequency of
the RF signal was 40 MHz, i.e., the spatial interval 𝛿z ofthe signal was 19.25 µm by assuming the speed of soundc0 to be 1,540 m/s, the frame rate was 286 Hz, and thebeam interval 𝛿x was 150 µm. The width (2N + 1) points
for obtaining the correlation in Eq. (5) was set to 21 points,
i.e., the actual width w was 385 µm. The factor M in theinterpolation of Rn (d0 ) of Eq. (5) was set to 10.
The plaque formed in the right carotid sinus of a patientwith dyslipidemia in his 50s was measured three times (inMarch 2012, December 2012, and March 2013). The target
region with width w was set in the plaque at every 𝛿z , andthe number of the target regions set along the ultrasonicbeam depended on the thickness of the wall. The minimum to maximum numbers of the target regions set along
the ultrasonic beam distributed along the lateral direction
were 47–96, 30–91, and 66–104 for the respective threemeasurements. For comparison, the right CCA of a healthy
male in his 20s was also measured.
The study protocol was approved by the ethics committee of the Graduate School of Engineering, Tohoku University (19A-5), and the participants agreed to participate
in this study.

Results and discussion
Results for the healthy CCA​
Figure 1a shows the analyzed region set between the two
red lines of the posterior wall on the B-mode image of
the CCA of a healthy subject. Since the thickness of the
IMC of the{ healthy
subject was thin (385 µm), the number}of targets d0 along the ultrasonic beam for the evaluation of the strain of Eq. (3) and elasticity of Eq. (4) was
set to be one. Along the lateral direction for the IMC, 47

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Journal of Medical Ultrasonics (2022) 49:529–543

targets were set. Figure 1b and c shows the distribution( )of their correlation Rndmax (d0 ) of Eq. (5) and strain 𝜀 d0
of Eq. (3), respectively.
Figure 1d shows( the) relationship( )between {Rndmax d0 } and brightness {B0 d0 } at the time of
the R-wave for 47 targets. Figure( ) 1e shows the relationshipbetween {Rndmax (d0 )} and {𝜀 d0 }.
Figure 1f–j shows the waveforms obtained during one
cardiac cycle in the IMC along the ultrasound beam shownby the white line in Fig. 1a. Figure 1f shows the ECG,
Fig. 1g shows the correlation Rn (d0 ) of Eq. (5), Fig. 1hshows the axial displacements zd0 − w (n) and zd0 + w (n) at the22lumen and adventitia sides of the vessel wall, respectively;
Fig. 1i shows the change Δhd0 (n) in thickness of Eq. (2)from the time of the R-wave, and Fig. 1j shows the lateraldisplacement x(n) from the time of the R-wave.
For the CCA of the healthy subject, the correlation
Rndmax (d0 ) of Fig. 1b was( )higher than 0.7 for all the lateral positions, strain 𝜀 d0 of Fig. 1c was almost constant( )at approximately –0.07, and brightness values B0 d0 of
Fig. 1d ranged from –16 to –10 dB. As shown in Fig. 1g,
the correlation Rn (d0 ) was always maintained at high values
during one cardiac cycle. As shown in Fig. 1i, the change inthe wall thickness,Δhd0 (n), became approximately −25 µmwith vessel dilatation and then returned to the original zero.
As shown in Fig. 1j, the maximum displacement of the CCA
in the lateral direction was approximately 1 mm for the heartside.
The waveforms for the change in thickness, Δhd0 (n), ofFig. 1i, Rn (d0 ) of Fig. 1g, and the lateral displacement x(n)of Fig. 1j were obtained during one cardiac cycle for all
ultrasound beams. From these results, the CCA became
homogeneously thinner with dilatation and then returned tothe original level, the correlation was high, and CCA homogeneously moved in the lateral(direction
to the heart side in)systole. Therefore,
thestraininFig.
1c and the elastic
𝜀
d
0
( )
modulus Eθ d0 of Eq. (4)reliable for the CCA of the( were)healthy subject, and Eθ d0 = 673 kPa and the correlation
Rn (d0 ) of Fig. 1g did not decrease, although there was alateral displacement of about 1 mm.

Results for the plaque for the patient
For the RF data measured in March 2013 for the patient,Fig. 2a shows the analyzed region set between the two redlines on the B-mode image of the plaque of the carotid
sinus. In this region, 4115 targets were set, and the analysis described above was applied for each target. Figure 2b
shows the distribution( ) of the correlation {Rndmax (d0 )} and thebrightness{B
0 d0 } at the time of the R-wave (0th frame).
( ){B0 d0 } in Fig. 2b ranged more widely than that for thehealthy CCA in Fig. 1d. This is because the brightness tends

Journal of Medical Ultrasonics (2022) 49:529–543

(a)

(b)

(c)

Fig. 2  a B-mode image of a plaque at the carotid sinus of a patientand analyzed region between the two red lines. For 4115
( )targets in theanalyzed region, b distribution of correlation {Rndmax d0 } and bright( )( )( )ness {B0 d0 }, and c distribution of {Rndmax d0 } and strain {𝜀 d0 }535

to be higher for the interface between harder tissues andsofter tissues, and the plaque has both soft and hard tissues,
which corresponds to the already known fact that the plaquehas a heterogeneous structure.
{ (Figure)} 2c shows the distribution {Rndmax (d0 )} and strain
𝜀 d0 for 4115 targets. There were targets in areas II and
III with a low correlation( ) Rndmax (d0 ) and in areas I and II
with positive strain 𝜀 d0 for the plaque, whereas the target
was not observed in these areas I–III for the healthy CCA
in Fig. 1e.
For the same data, Fig. 3a and b shows the cross-section( )images of the correlation {Rndmax (d0 )} and strain {𝜀 d0 },respectively. By comparing these images, targets (red or
yellow) with positive strain in Fig. 3b have not only a small
correlation (blue or green) but also a high correlation (redor orange) in Fig. 3a.
Along the same ultrasonic beam, two targets A and B set
in Fig. 3a and b were analyzed in detail as follows, whered0A and d0B are the center depths in( A and) B, respectively.
For A, Rndmax (d0A ) = 0.94
and𝜀d
0A > 0 , and for B,( )Rndmax (d0B ) = 0.84 and 𝜀 d0B < 0. Figure 3c and d shows theRF signals for targets A and B at the time (0th frame) of the
R-wave and at the time (ndmax-th frame) of the maximum dilatation, respectively. The correlation was high for both targets.
Figure 3e–j shows the detailed results (waveforms) fortargets A and B during one cardiac cycle. Figure 3e shows
the ECG, and Fig. 3f shows Rn (d0 ) during one cardiac
cycle in each target. Figure 3g and h shows the measured
axial displacements zd0A (n) and zd0B (n) , Fig. 3i shows thechanges in thickness Δhd0A (n) and Δhd0B (n) , and Fig. 3jshows the measured lateral displacement x(n) of the entire
vessel wall. For target A, Rndmax (d0A ) of Fig. 3f remained
high and Δhd0A (n) of Fig. 3i returned( ) to the original level
after one cardiac cycle, but 𝜀 d0A > 0 . Thus, for A, thechange in thickness( ) is unsuitable for estimation of the elastic modulus Eθ d0 using Eq. ((4). )Alternatively, for B, Rndmax d0B = 0.84 was high, andΔhd0B (n) of Fig. 3i became approximately 15 µm thinnerand returned to its original value at the time of the succeeding R-wave. As shown in Fig. 3j, the maximum displacement of the vessel in the lateral direction was 109 µm,
which is smaller than the beam spacing of 150 µm. If thelateral displacement affects the RF signal for the plaque, thecorrelation may decrease. However, for both targets A and
B, Rndmax (d0 ) remained large during one cardiac cycle, butchanges in thickness, Δhd0A (ndmax ) and Δhd0B (ndmax ), werecompletely different even though A and B were on the samebeam.
Therefore, the displacement of the plaque in the lateral
direction caused by vessel dilatation and/or heart contraction
does not have a critical influence on the change in the RF
signal, and other factors may decrease the correlation. The
plaque in Figs. 2 and 3 included targets where the correlation

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Journal of Medical Ultrasonics (2022) 49:529–543( )targets, the targets with positive strain ( 𝜀 d0 > 0) and high ▸correlation ( Rndmax (d0 ) ≥ 0.7) and their surroundings were set
as regions R1–R5 with red frames. The expanded figure foreach of R1–R5 is shown in Fig. 4(1-a)–(5-a), where the subregions with( ) high correlation ( Rndmax (d0 ) ≥ 0.7) but positive
strain (𝜀 d0 > 0) are surrounded by a black dashed( line.
)Figure 4b shows the brightness change ΔBndmax d0 fromthe time of the R-wave to the time of maximum vessel dilatation for the same set of regions R1–R5. Similar to Fig. 4(1a)–(5-a), Fig. 4(1-b)–(5-b) shows thefigure for( expanded)
each of R1–R5 in Fig. 4b for ΔBndmax d0 .
Figures 5 and 6 show the analyzed results for the second
and third data from the carotid sinus of the same subject
measured on two different days, respectively (December
2012 for Fig. 6, and March 2013 for Fig.
( 5).
) Figure 5a andb shows the distributionsofstrain𝜀d0 and brightness( )changes ΔBndmax d0 for the second data, and Fig. 6a andb shows their distributions for the third data. For theseimages, as shown in Fig. 4, after excluding targets with low( )Rndmax (d0 ) was high but the strain 𝜀 d0 was positive. Thesetargets are not suitable for measuring the elastic modulus.
However, it is not possible to identify these targets only fromthe correlation values.

Typical patterns for regions with positive strain
despite high correlation in RF signals
As shown in target A in Fig. 3,( in) the plaque, there weresome targets where the strain 𝜀 d0 was positive at the timeof maximum dilatation, while the high correlation Rn (d0 )was maintained during one cardiac cycle. For such(targets,)
let us observe the change in brightness, ΔBndmax d0 , ofEq. (6) from the time of the R-wave to the time ndmax at the
maximum dilatation as follows:
In Fig. 4a, for the same data as Figs. 2 and 3, the targets
with low correlation ( Rndmax (d0 ) < 0.7) were excluded fromthe detailed analysis and filled with gray; for the remaining

(e)
(a)
(f)

(b)

(g)

(c)

(h)

(d)

(i)

(j)

Fig. 3  For the same data of the arterial wall in Fig. 2, the( )crosssectional images of a correlation Rndmax (d0 ) and b strain 𝜀 d0 . c, dRF signals for targets A and B at the time of R-wave and at the timeof the maximum dilatation, respectively. For targets A and B set in13

a and b, the waveforms of e the ECG, f the correlation Rn (d0 ), g, h
the measured axial displacements zd0 (n), i the changes in thickness,
Δhd0 (n), and j the measured lateral displacement x(n) of the entire
region during one cardiac cycle

Journal of Medical Ultrasonics (2022) 49:529–543( )Fig. 4  The cross-sectional( ) images of a strain 𝜀 d0 and b change
in brightness, ΔBndmax d0 , for the target regions of high correlation( Rndmax (d0 ) ≧ 0.7) of RF signals on the cross-sectional image of theplaque. The targets with low correlation ( Rndmax (d0 ) < 0.7) are filled( )with gray. Five regions R1–R5 where strains 𝜀 d0 are positive aredenoted by the red frames. For each of the regions R1 to R5, (1)–(5)537show a thecross-sectional images of the distribution of the( magnified)
strains {𝜀 d0 }, b the magnified images of the distribution of changes( )in brightness, {ΔBndmax d0 }, c an illustration for explanation, and d( )( )distribution of correlation {Rndmax d0 } and {ΔBndmax d0 } for targets
in each region. In c and d,( the) color( of)each plotted(point) is distinguished by the values of 𝜀 d0 , Rndmax d0 , and ΔBndmax d0

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Journal of Medical Ultrasonics (2022) 49:529–543

Fig. 5  For the second data from( )the carotid sinus of the same subject, a, b (1)–(4) are shown in a format similar to Fig. 4. In a and b, four
regions R6–R9 where strains 𝜀 d0 are positive are denoted by the red frames

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Journal of Medical Ultrasonics (2022) 49:529–543

correlation ( Rndmax (d0 ) < 0.7), for the remaining targets, thetargets with( )high correlation ( Rndmax (d0 ) ≧ 0.7) and positive
strain (𝜀 d0 > 0) and their surroundings are defined as four
regions R6–R9 for Fig. 5a and b, and five regions R10–R14
for Fig. 6a and b.
( )From the observations using regional strain 𝜀 d0 of
Eq. (3), the correlation( )Rndmax (d0 ) of Eq. (5), and the brightness change ΔBndmax d0 of Eq. (6), we found that all of the
14 regions (R1–R14) with high correlation but positive strain
and their surroundings in Figs. 4, 5, and 6 were classified
into one of the following three characteristic patterns I—III,
as illustrated in Fig. 7a–c.
For Pattern I,(the)sub-region (yellow) with high( correla)||tion and |ΔBndmax d0 | < 5 dB but positive strain (𝜀 d0 > 0)||at the center is surrounded by the(blue) where( sub-region
)
dB)
with
negativethe brightness
increases
(
ΔB
d
>
5
ndmax
0
( )
strain (𝜀 d0 < 0). For Pattern II, inside thesub-region(yel( )||low) with high correlation and |ΔBndmax d0 | < 5 dB but||( )positive strain (𝜀 d0 > 0), there (is a)sub-region (red) where
the brightness increases (ΔBndmax d0 > 5 dB) with positive
strain. For Pattern III, inside( the)| sub-region (yellow) with|high correlation and |ΔBndmax d0 | < 5 dB but positive strain||( )(green) where the bright(𝜀 d0 > 0), there is a sub-region( )ness decreases (ΔBndmax d0 < −5 dB) with positive strain.
These sub-regions are surrounded by the sub-region (gray)with low correlation ( Rndmax (d0 ) < 0.7).
For regions R1 in Fig. 4(1), R3 in Fig. 4(3), and R4 in
Fig. 4(4), the sub-region (yellow in Fig. 4(1-c),( )| (3-c), and|(4-c)) with high correlation and |ΔBndmax d0 | < 5 dB but||
positive strain at the center was surrounded by the subregion ( (blue)
where the br ightness increased)(ΔBndmax d0 > 5 dB), which was classified into Pattern I.
For regions R2 in Fig. 4(2) and R5 in Fig. 4(5), inside thesub-region (yellow in( Fig.
)| 4(2-c) and (5-c)) with high cor|
relation and |ΔBndmax d0 | < 5 dB but positive strain, there||
is a sub-region
(red)
where
the brightness increased( )(ΔBndmax d0 > 5 dB), and these regions were classified into
Pattern II.
Similarly, for Fig. 5, regions R6 in Fig. 5(1) and R9 in
Fig. 5(4) were classified as Pattern I, and regions R7 in
Fig. 5(2) and R8 in Fig. 5(3) were classified as Pattern II. In
Fig. 6, region R14 in Fig. 6(5) was classified into Pattern I,
region R13 in Fig. 6(4) was classified as Pattern II, andregions R10 in Fig. 6(1), R11 in Fig. 6(2), and R12 in Fig. 6(3)were classified as Pattern III. Thus, 16 regions with( )|high|
correlation values ( Rndmax (d0 ) ≧ 0.7) and |ΔBndmax d0 | < 5||( )dB but positive strains ( 𝜀 d0 > 0 ) analyzed in Figs. 5, 6,
and 7 were roughly classified( into) one of the three patterns
using Rndmax (d0 ) and ΔBndmax d0 .
Therefore, it is possible( ) to roughly evaluate whether
the measured strain 𝜀 d0 is appropriate for estimating the539

elastic modulus. For plaque, not only the region where thecorrelation Rndmax (d0 ) between the RF signals is low but also
the region classified into one of the Patterns I, II, and III are
unsuitable for estimation of the elastic modulus even when
the correlation value Rndmax (d0 ) is high and brightness does
not change; i.e., the RF signal maintains its waveform andamplitude during one cardiac cycle.

Conclusion
In this study, the local changes in waveforms of RF signals
and brightness inside the plaque caused by vessel dilatation
were thoroughly observed to identify the targets where thestrain measurement is unreliable for obtaining the elastic
modulus of the plaque. For the healthy CCA,( )the change in
the RF signals was small, and the strain 𝜀 d0 was negative
for all lateral positions. In contrast, for the plaque of thepatient, there were some targets with large local changes( )in the RF signals. In these targets, the obtained strain 𝜀 d0
was positive, whichthat the calculation of the( indicated)elastic modulus Eθ d0 was not suitable.
Furthermore, there were some regions where the( change)
in RF signals was sufficiently small but the strain 𝜀 d0 was
positive. These regions were classified into one of three specific patterns characterized by (the)correlation Rndmax (d0 ) andthe brightness change ΔBndmax d0 , as illustrated in Fig. 7.
Thus, not only targets with a low correlation Rndmax (d0 )where the RF signals largely changed in waveform withvessel dilatation but also targets that were classified into
one of the specific patterns
unsuitable for estimat( were)
ing the elastic modulus Eθ d0 , even though the correlation
Rndmax (d0 ) was high during vessel dilatation.
As a preliminary study, this study provides a clue toassert the reliability of elasticity estimation inside plaque.
Further research on the increase in the number of patterns
by applying the method to many plaques from patientsis necessary to ascertain the reliability more accurately.
Another future study can consider elucidating the causesof these specific patterns of brightness change in the region
where the correlation between the RF signals is high but thestrain is positive.

Appendix: Derivation of the local elasticityof the arterial wall and the assumptions
in Eq. (4)( )In the estimation of the local elastic modulus Eθ d0 , it isassumed that the vessel wall is elastically incompressible(Poisson ratio 𝜈 = 0.5) and isotropic; the strain of the vessel wall in the axial direction, 𝜀z , can be negligible (𝜀z = 0)

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Journal of Medical Ultrasonics (2022) 49:529–543

Fig. 6  For the third data(from) the carotid sinus of the same subject, a, b (1)–(5) are shown in a format similar to Fig. 4. In a and b, five regions
R10–R14 where strains 𝜀 d0 are positive are denoted by the red frames

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541

because the artery is strongly restricted in the axial direction
in vivo; and the change of inner radius Δr and the changeof target thickness Δhd are sufficiently small compared tothe initial radius r0 and the target thickness w at the time of
R-wave, respectively. It is also assumed that the pressure in
the vessel wall changes linearly from the pressure on the
inner surface of the vessel wall (i.e., internal pressure oflumen) to the pressure outside the vessel (i.e., atmosphericpressure).
From the(assumptionof elastic isotropy, the local elastic)
modulus Eθ d0 in the circumferential direction on the local
target set around the center depth d0 with width w along theultrasonic beam inside the wall is defined as [30]
( ) (
( )
( )
( ))
Eθ d0 = Δ𝜎r d0 − 𝜈Δ𝜎θ d0 − 𝜈Δ𝜎z d0 𝜀 1d .[Pa]
( 0)
(A1)
( )
The first term Δ𝜎r d0 in Eq. (A1) is the time change ofstress in the radial direction at a depth d0 . The second andthird( terms) are the contribution of time changes (of stresses)Δ𝜎θ d0 in the circumferential direction( ) and Δ𝜎z d0 in theaxial direction to the radial strain 𝜀 d0 at depth d0.
The radial stress 𝜎r (d0 ) is obtained by the averageof stresses on the lumen and adventitia sides of the( tar)
get. Under the assumptions mentioned above, Δ𝜎r d0 is
obtained as [31]
{
)
)}
(
(
( )
Δ𝜎r d0 = − 12 Δp� d0 − w2 + Δp� d0 + w2
, [Pa] (A2)

(a)

(b)

where h0 ≥ w is the initial thickness of the vessel wallat the time of R-wave and Δp� (d) is the time change of thepressure on depth d inside the wall. Under the assumptionof linearity of pressure change in the wall [31], Δp� (d) canbe expressed using the pulse pressure Δp (time change ofinternal pressure of lumen minus atmospheric pressure)measured by a sphygmomanometer asΔp� (d) =h0 −(d−dw )h0Δp.[Pa](A3)

From the conditions for the equilibrium of forces in theradial direction on the target and the assumptions mentioned
above, Δ𝜎θ (d0 ) is obtained as [31]
(
)
(
)
( )
Δ𝜎θ d0 = w1 r0 + d0 − w2 − dw Δp� d0 − w2
(
)
(
)
(A4)
− w1 r0 + d0 + w2 − dw Δp� d0 + w2 , [Pa]where dw < d0 is the depth of the interface between thelumen and the inner surface of the vessel wall at the timeof R-wave. The first and second terms of Eq. (A4) are thecontributions of pressures on the lumen side surface and theadventitia side surface of the target, respectively. Δ𝜎z (d0 ) is
obtained from the assumption of 𝜀z = 0 as [30]
( ))
( )
(
( )
Δ𝜎z d0 = 𝜈 Δ𝜎r d0 + Δ𝜎θ d0 .[Pa]
(A5)

(c)

( )
Fig. 7  aI, b pattern II, and c pattern III for explaining the sub-regions (yellow) with positive strain 𝜀 d0 and high correlation( Pattern)( Rndmax d0 ≧ 0.7) and the typical surroundings

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By substituting Eqs. (A2,( )A3, A4, A5) into Eq. (A1), thelocal elastic modulus Eθ d0 on the target is obtained as( ) {()( )( )} 1Eθ d0 = 1 − 𝜈 2 Δ𝜎r d0 − 𝜈(1 + 𝜈)Δ𝜎θ d0
( )
𝜀 d0
( )
( )) 13(= −Δ𝜎r d0 + Δ𝜎θ d0
( )
4
−𝜀 d0
(
) w
w
Δp
h0
3 1 r0 + d0 − 2 − dw=+( ) .[Pa]
4 2
w
−𝜀 d0
(A6)
Equation (A6) is the expansion of the elasticity definition
derived by Hasegawa et al. [30] and equals the elasticity
for the entire wall [30] by substituting d0 = dw + h0 ∕2 andw = h0 into Eq. (A6). Thus, Eq. (4) is derived.
Acknowledgements The present work was supported in part by
the Japan Society for the Promotion of Science KAKENHI Grants
20H02156 and 19KK0100.

Declarations
Conflict of interest The authors declare that they have no competinginterests.
Ethical statement All the procedures followed were performed under the
ethical standards of the responsible committee on human experimentation(institutional) and with the Helsinki Declaration of 1964 and later versions.

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