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Accuracy verification in ultrasonic elasticity measurement within intimamedia complex visible range using phantom experimental system
To cite this article: Seira Akiyama et al 2021 Jpn. J. Appl. Phys. 60 SDDA07

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REGULAR PAPER

Japanese Journal of Applied Physics 60, SDDA07 (2021)
https://doi.org/10.35848/1347-4065/abef0d

Accuracy verification in ultrasonic elasticity measurement within intima-media
complex visible range using phantom experimental system
Seira Akiyama1, Shohei Mori2*, Mototaka Arakawa1,2, and Hiroshi Kanai1,2
1Graduate School of Biomedical Engineering, Tohoku University, Sendai, Miyagi 980-8579, Japan
Graduate School of Engineering, Tohoku University, Sendai, Miyagi 980-8579, Japan2*

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

Received December 1, 2020; revised February 10, 2021; accepted March 16, 2021; published online April 7, 2021
Studies to investigate the ultrasound elasticity measurement of the carotid artery, for early detection of arteriosclerosis, are ongoing. In the longaxis cross-sectional measurement in vivo, the position where the intima-media complex (IMC) is visible on the B-mode image was assumed to be
the central axis of the short-axis view of the carotid artery. However, the IMC is also visible near the central axis of the short-axis view of the carotid
artery. In the present study, accuracy in elasticity measurement within the IMC visible range was evaluated through a phantom experiment. The
elasticities of the posterior wall measured at plural points within the IMC visible range differed by up to 6%. From the experimental results, weconcluded that for the highest accuracy, it is important to measure along the central axis of the short-axis view of the carotid artery.
© 2021 The Japan Society of Applied Physics

1. Introduction

Cardiovascular diseases such as strokes and myocardial infarctions are the leading causes of death worldwide;1) these diseases
are caused primarily by arteriosclerosis. In the early stages ofarteriosclerosis, the cholesterol content in the aorta affects theelasticity of the arterial wall; therefore, measuring the elasticityof the arterial wall can aid early detection of arteriosclerosis.2)
Diagnostic methods for arteriosclerosis include angiography, angioscopy, intravascular ultrasound, and radiographic imaging.3) As these diagnostic techniques are invasive, they are not suitable for non-invasively andrepetitively diagnosing changes over time in the early stagesof arteriosclerosis. Non-invasive methods for diagnosing
arteriosclerosis include magnetic resonance imaging, intima-media complex (IMC) thickness (IMT) measurement
using ultrasound,4) and blood ﬂow measurement using
ultrasound. Because these diagnostic methods mainly measure information such as the shape of the arterial wall, thesize of the atherosclerotic plaque, and the degree of stenosis,
it is difﬁcult to diagnose the histological characteristics.
Elasticity measurement is one of the approaches forevaluating the tissue characteristics of the arterial wall.5–11)
Non-invasive evaluation methods for determining the elastic
properties of the arterial wall include pulse wave velocity
measurement,12,13) stiffness parameter measurement,14,15)
and ﬂow-mediated dilation.16) These methods can be used
to evaluate the average elastic properties of the entire wall.
To measure the local elasticity of the arterial wall using
ultrasound, the change in thickness of the arterial wall ismeasured in a local region, approximately 0.1 mm in thelong-axis direction of the blood vessel.17–21) This method canmeasure the distribution of local elasticities and evaluate thehistological characteristics of heterogeneous atherosclerotic
plaques. Kanai et al. developed the phased tracking method
to measure the minute displacement of the arterial wall in one
heartbeat.22) The elasticity of the arterial wall can be
estimated from the thickness change measured from theminute displacement of the arterial wall and the pulsepressure measured by a sphygmomanometer. Kanai et al.
presented an elasticity tomographic image by measuring the
local elasticity of the carotid artery.23) Inagaki et al.

developed a method for tissue characterization of the arterial
wall by analyzing the elasticity distribution of the tissue
illustrated by the elasticity tomographic image.24)
As the true value of elasticity is unknown in vivo, themeasurement accuracy cannot be veriﬁed in vivo. Therefore,
the measurement accuracy of elasticity was veriﬁed throughphantom experiments in a previous study. In vivo, elasticity
was measured on the long-axis view of the carotid artery byassuming that the position where the IMC is visible corresponds to the central axis of the short axis of the carotid artery.
Therefore, the elasticity of the phantom was also measured on
the long-axis view in that study.25) However, the position
where the IMC can be seen is not always the central axis; theIMC can be observed in the vicinity of the central axis in the
short-axis view of the carotid artery. Therefore, it is important
to assess the accuracy of elasticity measurement within the
IMC visible range. For this purpose, it is necessary to validate
the elasticity measurement accuracy in the short-axis view,
where the position of the central axis can be identiﬁed.
In our previous study,26) we conducted a phantom experiment to evaluate the accuracy of ultrasound elasticity
measurement on the central axis of the short-axis view.
However, the elasticity measurement accuracy in positionsneighboring the central axis has not been examined yet.
In the present study, the accuracy of elasticity measurement within the IMC visible range was veriﬁed. First, the RF
signal measured on the central axis of the short-axis view wasanalyzed, and the elasticity was estimated. The elasticity wascalculated using the external radius change, and the result
was compared with that of the laser sensor measurement.
Then, the elasticity calculated using the change in thickness
was compared with that calculated using the external radiuschange in the ultrasound measurement. Finally, elasticity wasmeasured at positions deviated from the central axis of theshort axis of the phantom; it was then compared with theelasticity measured along the central axis.
2. Principles
2.1. Measurement of elasticity using thickness
change (ultrasound)

The change in arterial wall thickness Dh (t ) that occurs withpulsation is measured by the phased tracking method.22)

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S. Akiyama et al.

Assuming that the arterial wall is elastically incompressible27)
and isotropic and the artery is strongly restricted in the longitudinal direction (i.e. the strain in the longitudinal direction is
negligible), the elastic modulus Eqh in the circumferential
direction is expressed by Eq. (1) as follows:28–30)
Eqh =

3⎛
2r0 ⎞ Dp
,
⎜1 +
⎟
8⎝
h 0 ⎠ - Dh

re =

h0

E inc =

3 r02 Dp,
2 re2 - r02 Dre

(2 )

re

where re is the external radius before deformation.
Equation (2) can also be derived from Eq. (1) by introducing
the assumptions that the wall thickness is uniform in thecircumferential direction, Dre (t )2  re2, Dr0 (t )2  r02, andh 02  (2r0 )2 .
From the relationship between the incremental internal pressure Dp (t ) and the incremental strain Dre (t ) /re, the slope forone cycle of circulation Dp / {Dre /re} was estimated using theleast-squares method to obtain Einc. Therefore, the term
Dp / {Dre /re} on the right side of Eq. (2) becomes a timeindependent constant. For measurement using the laser sensor,
the initial arterial radius r0 was calculated as the difference
between the external radius re (before the deformation) measured
by the laser sensor and the initial thickness h 0 measured by theultrasound; the external radius change Dre (t ) was measured by
the laser sensor. To compare the result of the ultrasound with thatof the laser sensor, Einc was also estimated in the ultrasoundmeasurement. In the ultrasound measurement, the initial arterial
inner radius r0, the external radius before the deformation re, andthe external radius change Dre (t ) were measured using ultrasound.
2.3. Sound velocity estimation in phantom
The initial thicknesses hant and h pos of the anterior and posterior
walls, respectively, the inner radius r0, and the external radius reof the phantom in Eqs. (1) and (2) are expressed in terms of thesound velocity cp of the phantom as follows:
hant = cp tant ,

(3 )

(4 )

cw tlum
,
2

(5 )

r0 =

(1 )

where h 0 is the initial thickness, r0 is the initial arterial inner
radius, and Dp (t ) is the incremental internal pressure. From
the relationship between the incremental internal pressure
Dp (t ) and the incremental strain -Dh (t ) /h 0 , the slope forone cycle of circulation Dp / {-Dh /h 0} was estimated using
the least-squares method to obtain Eqh. Thus, the term
Dp / {-Dh /h 0} on the right side of Eq. (1) becomes atime-independent constant. The initial thickness h 0 , the initialarterial inner radius r0, and the change in the arterial wall
thickness Dh (t ) were measured through ultrasound.
2.2. Measurement of elasticity using external
diameter change (laser and/or ultrasound)
Since the thickness change cannot be measured by a laser
sensor, the elasticity was measured using the external
diameter change. Assuming that the wall thickness is uniform
in the circumferential direction, the incremental elasticity Einccan be calculated using the external radius change Dre (t ) of
the phantom, as expressed by Eq. (2)31)

h pos = cp tpos,

cw tlum + cp (tant + tpos )
2

,

(6 )

where cw is the speed of sound in water and tant, tlum, and tpos
are the propagation times of the ultrasound pulse in the anteriorwall of the phantom, the phantom lumen, and the posterior wallof the phantom, respectively. In the present study, cw wasmeasured using water temperature.32) From Eqs. (1)–(6), it isclear that knowledge of the sound velocity cp of the phantom isnecessary for elasticity measurement. This estimated soundvelocity cp was used for introducing the initial thickness h 0 , theinitial arterial inner radius r0, and the change in the arterial wall
thickness Dh (t ) in Eq. (1), and the initial arterial inner radius r0,
the external radius before deformation re, and the external radiuschange Dre (t ) in Eq. (2). Therefore, the sound velocity of thephantom was estimated using the RF signal obtained from anacrylic block placed under the phantom in water.
Figure 1 illustrates (a) the schematic of the experiment formeasuring the phantom sound velocity, (b) the schematic of
the B-mode image obtained by using the experimental
conﬁguration in Fig. 1(a). In this condition, the ultrasoundpropagation times from the probe to the acrylic block at
positions p1 and p2 , depicted in Fig. 1(b), are different due tothe difference in sound velocities of the water and thephantom. Therefore, the visualized depth of the acrylic blockon the conventional B-mode image, which assumes aconstant sound velocity, is changed by the lateral position,
as depicted in Fig. 1(b). The sound velocity of the phantom
can be measured by comparing the propagation times of thetwo ultrasound beams depicted by yellow lines, which aremeasured along with positions p1 and p2 . The distance x1
from the probe to the acrylic block at position p1 and x2 fromthe probe to the acrylic block at position p2 are expressed by
Eqs. (7) and (8), respectively
x1 = cw (t1 - tant - tpos) + cp (tant + tpos) ,

(a)

(7 )

(b)

Fig. 1. (Color online) (a) Schematic for estimation of sound velocity cp inphantom and (b) schematic of the B-mode image under experimental
conﬁguration in Fig. 1(a).

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Jpn. J. Appl. Phys. 60, SDDA07 (2021)

x2 = cw t2,

S. Akiyama et al.

(8 )where t1 and t2 are the propagation times of the ultrasoundpulse from the probe to the acrylic block at positions p1 andp2 , respectively. Because the distances x1 and x2 from theprobe to the acrylic block are equal, as depicted in Fig. 1(a),the sound velocity cp of the phantom can be calculated from
Eqs. (7) and (8), as shown in Eq. (9)⎛t - t2 ⎞⎟.
cp = cw ⎜1 - 1
tant + tpos ⎠⎝Fig. 3. (Color online) Schematic of laser sensor measurement.

(9 )3. Experimental method

Figure 2 shows (a) the schematic of the experimental systemand (b) the setting of the ultrasound probe and the laser
sensor. Figure 2(b) is a side view of Fig. 2(a). The ultrasoundmeasurement was conducted using an ultrasonic diagnostic
device (SSD-6500, Aloka, Japan). A linear probe with acentral frequency of 7.5 MHz was used. The values of thesampling frequency, beam spacing, and frame rate were
40 MHz, 150 μm, and 286 Hz, respectively.
Figure 3 shows a schematic of the laser sensor measurement. The laser displacement meter (IG-028, KEYENCE,
Japan) used in the study, which is composed of a lighttransmitter and a light receiver, can measure the length of thearea where laser light is blocked, that is, the external diameterof the phantom.
A black silicone tube (Shonan Kasei, Japan) with an
ASKER-C hardness of 10°, an external diameter of 9 mm,
an inner diameter of 7 mm, and a wall thickness of 1 mm
(nominal value) was used as a simulated carotid artery
phantom. Carbon powders with 5 wt% were included as
scatters in the tube. In the estimations of elasticity using
Eqs. (1) and (2), these nominal values were not used, as
described in Sects. 2.1 and 2.2. The ASKER-C hardness wasmeasured by a durometer (ASKER-C) speciﬁed by theSociety of Rubber Science and Technology in Japan. A
pulsatile pump unit (EC-8, Fuyo, Japan) was used to simulate
the in vivo condition of blood circulation. The number ofpulsations was set to 60 times min−1. The water in theaquarium was degassed and puriﬁed; for circulation, tapwater was used.
The pressure sensor (PS-1KC, Kyowa, Japan) was used tomeasure the incremental internal pressure Dp (t ), which isused in Eqs. (1) and (2). Because the time delay of the
waveforms measured by the pressure sensors [presented inFig. 2(a) as (i) and (ii)] was sufﬁciently small, the pressure
measured by sensor (i) was used to calculate the elasticity.
In a previous study,26) the phantom was placed in air forthe laser sensor measurement because the measurement was
unstable when the phantom was placed in tap water; thisinstability was due to the scattering of the laser by dust andair bubbles in tap water. Because the ultrasound measurement
could not be conducted in the air, the measurement conditions were different between the laser sensor and ultrasoundmeasurements, and the measured waveforms of external
diameter change did not correspond for the two measurements. In the present study, the laser sensor measurement inwater was stabilized using degassed and puriﬁed water in thewater tank wherein the phantom was placed. Therefore, themeasurements could be conducted under the same conditions
using the ultrasound and the laser sensor, and the simultaneous measurement was realized. A sheet-shaped laser beam
was used to visually align the ultrasound beam with the laser
beam.
4. Results and discussion
4.1. Sound velocity estimation in phantom

Figure 4 shows the envelopes of the RF signals measured on
the ultrasound beams at positions p1 and p2 depicted inFig. 1. The propagation times t1 and t2 of the ultrasoundpulses from the ultrasound probe to the acrylic block at
positions p1 and p2 , respectively, and the propagation times
tant and tpos in the anterior and posterior walls of the phantom,
respectively, were measured from the peaks of the RF signal
envelopes. Then, the sound velocity cp of the phantom wasestimated as 1066 m s−1 using Eq. (9).
4.2. Accuracy verification of elasticity measurement
on central axis of short-axis view of phantom
Figure 5 shows (a) the B-mode image of the phantom in the
short-axis view, (b) the M-mode image on the central axis of
(b)

(a)

Fig. 2. (Color online) (a) Schematic of experimental system and (b) setting of the ultrasound probe and laser sensor.

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Jpn. J. Appl. Phys. 60, SDDA07 (2021)(a)

S. Akiyama et al.

(b)

Fig. 4. (Color online) Envelope of RF signal at positions of two ultrasoundbeams, p1 and p2 (Fig. 1) used for estimating the sound velocity cp inphantom.

the phantom, (c)(i) the incremental internal pressure Dp (t )measured by the pressure sensor and the incremental strain
Dre (t ) /re measured by the laser sensor or ultrasound, and (c)(ii) the incremental internal pressure Dp (t ) measured by thepressure sensor and the incremental strain -Dh (t ) /h 0
measured by the ultrasound. Each result presented in
Figs. 5(b) and 5(c) was measured along the central axis of
the short-axis view of the phantom [red line in Fig. 5(a)].
From Fig. 5(c)(i), the changes in the external radius Dre (t )correspond well in the ultrasound and laser sensor measurements. As depicted in Fig. 5(c)(ii), the thickness changes
Dh (t ) of the anterior and posterior walls are not congruent in
the ultrasound measurement.
Figure 6(i) depicts the relationship between the incremental internal pressure Dp (t ) measured by the pressure
sensor and the incremental strain Dre (t ) /re measured by theultrasound or laser sensor. Figure 6(ii) depicts the relationship between the incremental internal pressure Dp (t )(a)Fig. 6. (Color online) (i) Incremental internal pressure Dp (t ) and incremental strain -Dh (t ) /h 0 of anterior and posterior walls measured byultrasound and (ii) incremental internal pressure Dp (t ) and strain Dre (t ) /remeasured by ultrasound or laser. Results for three cycles of pulsation are
shown.

measured by the pressure sensor and the incremental strain-Dh (t ) /h 0 , measured by the ultrasound. The measurement
results for three cycles of pulsation are shown in Fig. 6. In
Fig. 6(ii), the measured hysteresis curves correspond wellwith the three measurements for the anterior or posterior
walls. However, the hysteresis curves of the anterior andposterior walls are not congruent because the incremental
strain -Dh (t ) /h 0 is different for the anterior and posterior
walls, as shown in Fig. 5(c)(ii).
To investigate the disagreement between the incremental
strains -Dh (t ) /h 0 of the anterior and posterior walls of thephantom, the phantom was rotated 180° concerning thecenter of the short-axis view, and the incremental strains-Dh (t ) /h 0 were measured using the ultrasound. Figure 7
depicts the internal pressure Dp (t ) and the incremental strain-Dh (t ) /h 0. Figure 7(a) depicts the incremental strain-Dh (t ) /h 0 at position A (anterior wall) and position B(posterior wall). Figure 7(b) depicts the same parameters as(b)

Fig. 5. (Color online) (a) B-mode image of short-axis cross-sectional view of the phantom, (b) M-mode image on the red line in Fig. 5(a), (c)(i) incremental
internal pressure Dp (t ) and incremental strain Dre (t ) /re measured by ultrasound and laser sensor, and (c)(ii) incremental internal pressure Dp (t ) andincremental strain Dh (t ) /h 0 on anterior and posterior walls measured by ultrasound. Figures 5(b) and 5(c) depict the measurement results on the central axis of
the short-axis view of the phantom and results for the ﬁrst cycle measurement of pulsation.

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S. Akiyama et al.

(a)

(b)

Fig. 7. (Color online) (a) Incremental internal pressure Dp (t ) andincremental strain -Dh (t ) /h 0 where point A is the anterior wall and point B
is the posterior wall and (b) incremental internal pressure Dp (t ) andincremental strain -Dh (t ) /h 0 where point B is the anterior wall and point A
is the posterior wall.

Fig. 7(a) after the phantom was rotated 180° from thecondition in Fig. 7(a).
Let us discuss the difference in the results at positions A
and B. The differences in incremental strains for positions A
and B might be due to unequal sound velocity distribution
caused by the inhomogeneity of the carbon used in
the present study. However, it is difﬁcult to separately
measure the sound velocities in the anterior and posterior
walls in the phantom because only the average sound velocityof the anterior and posterior walls can be computed using
Eq. (9). The wall thickness might also be unevenly distributed. Even if the wall thickness is uneven in thecircumferential direction, this difference does not affectthe estimation of elasticity because Eq. (1) does not require
the assumption of uniformity of the wall thickness
in the circumferential direction and considers the locality of
the initial wall thickness. Thus, we concluded that thedifference in the hysteresis loop between positions A and B
was caused by the difference in the actual elasticity and/orsound velocity at positions A and B of the phantom. The
locality of the actual elasticity and the sound velocity of thephantom in the circumferential direction will be examined infuture studies.
Table I presents the elasticities Einc calculated using thechanges in external radius Dre (t ) measured by the laser
sensor and ultrasound; it also shows the elasticities Eqh of theanterior and posterior walls calculated using the thickness
change Dh (t ) measured by the ultrasound. The elasticities
were measured for three different cycles of pulsation, and theaverage and standard deviation are shown in Table I.
The elasticities Einc, measured using the external radiuschanges Dre (t ) for the laser sensor and ultrasound measurements, agreed within 0.8%. This conﬁrmed that the accuracyof ultrasound elasticity measurement is similar to that of laser
sensor measurement when the ultrasound elasticity measurement is conducted along the central axis of the short-axis
view of the phantom.
In the ultrasound measurement, the elasticity Einc, measured
using the external radius change Dre (t ), and the average of theelasticities Eqh, measured using the thickness changes Dh (t )for the anterior and posterior walls, were within 0.05% of eachother. Therefore, the elasticity Einc, measured using theexternal radius change, represents the average of the elasticitiesof the anterior and posterior walls. The difference in elasticities
Eqh, calculated from the thickness change Dh (t ) on the anterior
and posterior walls, may reﬂect the inhomogeneity of elasticity
and/or the inhomogeneity of sound velocity in the phantom, as
discussed in Fig. 7. Thus, one advantage of ultrasoundmeasurement over laser sensor measurement is that it canmeasure the local elasticity.
4.3. Effect of measurement position within IMC visiblerange
We examined the effect of deviation of the measurement
position from the central axis of the short-axis view of thephantom on the elasticity measurement. Figure 8 shows (a)the B-mode image, (b) the maximum amplitude of theenvelope of the RF signals obtained from the intima of theposterior wall, and (c) the elasticities of the posterior wall at
plural positions in the lateral direction from the central axis of
the short axis of the phantom. The blue line in Fig. 8(b)shows the range of −6 dB bandwidth where the maximum
envelope amplitude of the posterior wall was 0 dB.
Figure 8(c) depicts the elasticities estimated in three measurements with different cycles of pulsation.
When the measurement position was outside of the −6 dB
bandwidth (i.e. outside of the enclosed region with bluelines), the elasticities decreased drastically. The reason forthis elasticity measurement error outside the IMC visible
range, depicted in Fig. 8(c), must be examined in futurestudies. For positions within the −6 dB bandwidth of theenvelope amplitude from the intima of the phantom (i.e.
inside the enclosed region with blue lines), the average values

Table I. Elasticity Einc calculated using the change in external radius Dre (t ) (laser, ultrasound) and elasticity Eqh calculated using thickness change Dh (t )(anterior wall, posterior wall).

Eqh [kPa] (ultrasound)
Einc [kPa] (laser)
507 ± 9

Einc [kPa] (ultrasound)

Anterior wall

Posterior wall

Average of anterior and posterior walls

511 ± 3535 ± 5488 ± 5512 ± 4

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S. Akiyama et al.

(a)

(c)

(b)

Fig. 8. (Color online) (a) B-mode image of short-axis cross-sectional view of the phantom, (b) envelope amplitude of intima of the posterior wall, and(c) elasticity of posterior wall measured on neighboring positions of the central axis of short-axis of the phantom.

of the posterior wall elasticity coincided within 6%. The
region enclosed by blue lines in Fig. 8 (i.e. −6 dB bandwidthof the envelope amplitude from the intima) approximately
corresponds to the IMC visible range in the in vivo
measurement. Therefore, the results presented in Fig. 8(c)indicate that the elasticity of the posterior wall of the carotid
artery can be measured with approximately 6% accuracy, if
the condition for the IMC visible range in the phantom
experiment of the present study is upheld in the in vivo
measurement (i.e. if the IMC is visible within 9° from thecentral axis in vivo). The causes of differences in estimatedelasticity within the IMC visible range may include theinﬂuence of refraction and the fact that the ultrasoundmeasures the projection component of h 0 , Dh (t ), and r0
when measuring on the neighboring position of the central
axis. In the short-axis measurement, these effects can be
examined quantitatively because distance from the central
axis can be measured. However, in the long-axis measurement, it is not possible to determine the distance fromthe central axis. Therefore, we concluded that for accurate
elasticity measurement, it is important to measure theelasticity along the central axis of the carotid artery inthe short-axis view.

ultrasound and laser sensor measurements, agreed within
0.8%. The elasticity Einc, calculated using the external radiuschange Dre (t ), and the average of the elasticities Eqh of theanterior and posterior walls, calculated using the thickness
changes Dh (t ), coincided within 0.05%. Finally, the elasticity was measured at positions deviated from the central axisof the short-axis view of the phantom. At positions corresponding to the IMC visible range in the in vivo measurement, the average values of the elasticity on the posterior walldiffered by up to 6%. We concluded that for accuracy, it isimportant to measure the elasticity along the central axis of
the carotid artery in the short-axis view.
In the future, we will examine an elasticity measurement
method that considers the refraction and projection components for measurements within the IMC visible range.
Moreover, the only guarantee for the stiffness of the phantom
used in the present study was ASKER-C hardness; therefore,
the accuracy of elasticity measurement was validated bycomparing the results of a laser sensor and ultrasoundmeasurements. Therefore, in future studies, Young’s modulusof the phantom must be determined through mechanicaltesting and compared with the ultrasound measurement
results.

5. Conclusions

Acknowledgments

In the present study, the accuracy of elasticity measurement
was assessed through phantom experiments using ultrasound.
First, sound velocity cp of the phantom used for the elasticity
measurement was estimated. Next, the elasticity of thephantom was measured using the sound velocity cp of thephantom, and the accuracy of the ultrasound elasticity
measurement along the central axis of the short-axis viewof the phantom was veriﬁed. The elasticities Einc calculatedusing the external radius changes Dre (t ), determined using

This work was supported in part by JSPS KAKENHI
19KK0100.

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