Ultrasound in Med. & Biol., Vol. 49, No. 3, pp. 875888, 2023
Copyright © 2022 World Federation for Ultrasound in Medicine & Biology. All rights reserved.
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https://doi.org/10.1016/j.ultrasmedbio.2022.11.014

 Original Contribution
LATERAL M-MODE: ULTRASOUND VISUALIZATION OF DISPLACEMENT ALONGLONGITUDINAL DIRECTION AT INTIMAMEDIA COMPLEXAGEDPST HOHEI MORI,* MOTOTAKA ARAKAWA,*,y and HIROSHI KANAI*,yTAGEDEN* Graduate School of Engineering, Tohoku University, Sendai, Japan; and y Graduate School of Biomedical Engineering, Tohoku
University, Sendai, Japan(Received 29 April 2022; revised 9 November 2022; in final form 19 November 2022)

Abstract—Quantification of the dynamics of the carotid artery wall is useful in evaluating arteriosclerosis andatherosclerosis. As the carotid artery wall moves not only in the radial direction but also in the longitudinal direction, longitudinal movement should be considered in the analysis of the dynamic properties of the carotid arterywall. In this study, we propose a “lateral M-mode” method for visualizing the longitudinal movement of the intimamedia complex (IMC). For the lateral M-mode, we set the target line in the longitudinal direction along the
IMC and visualize the signals on the target line frame-by-frame by correcting the position of the target line along
the radial displacement estimated by the phased tracking method. Differentiating the envelope signals between
consecutive ultrasound beams was effective in visualizing the lateral movement of the IMC. The precision of thelongitudinal displacement of the IMC estimated using the conventional block-matching method was validated bycomparing it with the lateral M-mode. Because the conventional M-mode sequence plays an important role inevaluation of the dynamics of various tissues, the proposed “lateral M-mode” contributes to a detailed understanding of vascular dynamics and the development of diagnostic methods for vascular diseases. (E-mail:mori@tohoku.ac.jp) © 2022 World Federation for Ultrasound in Medicine & Biology. All rights reserved.
Key Words: Ultrasound, Arteriosclerosis, Atherosclerosis, Intimamedia complex, Longitudinal motion, Lateral
M-mode, Block matching.

ultrasonically measured displacement of the carotid
artery wall in the radial direction caused by the propagation of pulse waves (Benthin et al. 1991; Kanai et al.
1994; Eriksson et al. 2002; Luo et al. 2012; Ito et al.
2018; Nagaoka and Hasegawa 2020).
To evaluate mechanical properties, measurement
methods for strain (Swillens et al. 2012), elasticity(Kanai et al. 2003; Hasegawa et al. 2004; Couade et al.
2010; Ramnarine et al. 2014; Salles et al. 2015) and viscoelasticity (Zhang et al. 2005; Arakawa et al. 2019;
Saito et al. 2020; Shoji et al. 2021) of the arterial wall
have been proposed. With these methods, radial and/or
longitudinal displacements of the arterial wall are measured to estimate each parameter. The luminal surface
roughness of IMC has also been studied as an indicator(Schmidt-Trucks€ass et al. 2003; Cinthio et al. 2011;
Kitamura et al. 2012; Nagai et al. 2014; Pozza et al.
2016). Kitamura et al. (2012) and Nagai et al. (2014)
proposed a method for measuring ultrasonically theluminal surface roughness of the carotid artery wall in
micron order, wherein the longitudinal displacement of
the IMC caused by pulsation is used to consider the

INTRODUCTION
The characteristics and mechanical properties of the
carotid artery are useful in diagnosing arteriosclerosis
and atherosclerosis (Grobbee and Bots 1994; Wada et al.
1994; Catalano et al. 2011; Boesen et al. 2015). Ultrasound diagnostic apparatus is a powerful tool for diseasediagnosis because of its non-invasiveness and real-time
performance. The intimamedia complex (IMC) thickness (IMT) measured from the B-mode image is a common indicator of the tissue characteristics of the carotid
artery wall (Grobbee and Bots 1994; Stein et al. 2008).
Pulse wave velocity (PWV) is an indicator of arterial
wall stiffness (Bramwell and Hill 1922). Several studies
have used ultrasound to measure PWV (Avolio et al.
1983; Benthin et al. 1991; Lehmann et al. 1992, 1993;
Kanai et al. 1994; Eriksson et al. 2002; Luo et al. 2012;
Ito et al. 2018; Nagaoka and Hasegawa 2020). In someof these studies, PWV has been estimated from theAddress correspondence to: Department of Electronic Engineering, Graduate School of Engineering, Tohoku University, Aramakiaza-Aoba 6-6-05, Sendai 980-8579, Japan. E-mail: mori@tohoku.ac.jp

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heterogeneity of the speed of sound in the ultrasoundpropagation medium from the skin to the carotid artery.
In this method, accurate measurement of the longitudinal
displacement of the IMC is essential.
Accurate measurement of the displacement of thearterial wall in the radial direction (i.e., ultrasound beam
direction) can be achieved using a phase-based velocity
estimator (Kanai et al. 1996; Hasegawa et al. 1998; Rabben
et al. 2002; Swillens et al. 2012; Pozza et al. 2016;
Akiyama et al. 2021). However, accurate measurement of
IMC displacement in the longitudinal direction is difficultin the early stage of arteriosclerosis because the thickness
and acoustic properties of the IMC are almost similar along
the longitudinal direction, and the difference in the envelope of the received ultrasound radiofrequency (RF) signals
in the longitudinal direction is small. To overcome these
difficulties, several studies have been conducted to estimate
the longitudinal displacement of the carotid artery wall, assummarized by Rizi et al. (2020). These studies haveapplied a block matching-based approach (Persson et al.
2002; Golemati et al. 2003; Cinthio et al. 2005, 2006,
2007; Zahnd et al. 2011; Idzenga et al. 2012; Yli-Ollila etal. 2013; Tat et al. 2016; Au et al. 2017, 2019), an approach
using the spatial phase information (Nilsson et al. 2013)
and a 2-dimensional (2D) cross-spectrum approach in thefrequency domain (Salles et al. 2015).
Although numerous techniques for estimating thelongitudinal displacement of the carotid arterial wall
have been studied and validated by simulations, phantom
experiments and reproducibility evaluations in in vivo
measurements, it is still difficult to confirm the actual
precision of the estimated longitudinal displacement inin vivo. One of the reasons may be the non-existence of amethod visualizing the longitudinal movement, whereas
the precision of the radial displacement measurement
can be confirmed by comparing it with the M-mode
image. The development of a method for visualization of
longitudinal movement contributes not only to the validation of the accuracy of the longitudinal displacement
estimation but also to the easy observation of the longitudinal wall motion by clinicians, as well as the use of conventional M-mode imaging for the observation of radial
wall motion.
To visualize the longitudinal movement of the IMC,
we focused on anatomic M-mode imaging (Strotmann etal. 1999) used in the field of echocardiography. An anatomic M-mode can set the target line for M-mode imaging in an arbitrary direction, as shown in Figure 1a;therefore, the displacement (A) along the target line canbe visualized, as shown in Figure 1b. In this anatomical
M-mode sequence, the target line is fixed at the same
position throughout the frames, similar to the conventional M-mode imaging.

Volume 49, Number 3, 2023

In several cases, however, the object moves in 2-D
directions, such as displacements (A) and (B), as shownin Figure 1a. In such cases, the position of the target line
should be corrected along the displacement (B). This
necessity was suggested by Carerj et al. (2003), but it
was not implemented.
In this study, we proposed a method for visualizationof the longitudinal displacement (A) of the IMC as “lateral
M-mode,” as shown in Figure 1c and 1d. To visualize longitudinal displacement (A), the target line was set along thelongitudinal direction, as shown in Figure 1c, based on anatomical M-mode imaging. Because the IMC moves in both
the radial and longitudinal directions, as shown in
Figure 1c, the position of the target line should be correctedalong the radial displacement (B) of the IMC. We applied
the proposed lateral M-mode imaging method to validate
the precision of the longitudinal displacement estimatedusing the conventional block-matching method.
METHODS
Principle: Setting the target line at the 0th frame forlateral M-mode imaging
Figure 2a illustrates a schematic of the B-mode imageof the posterior wall, and Figure 2b shows the actual Bmode image obtained for a healthy individual in his twenties.
The objective of the following procedure is to determine thedepth of the target line, z0 ðmÞ, on the mth beam at the 0thframe for the early stage of arteriosclerosis because it is difficult to estimate the longitudinal displacement in the earlystage, as described in the Introduction. To determine
fz0 ðmÞg as shown in Figure 2a, we set the depths fzb1 ðmÞgand fzb2 ðmÞg to include only the signal from the IMC, asfollows.
The arterial wall comprises intima, media and adventitia, as shown in Figure 2a. At the interface between thelumen and intima, the ultrasound is strongly scattered/reflected; therefore, a high-brightness region with a pulse
length is observed in the B-mode image. Because theintima and media have similar acoustic properties, ultrasound is not scattered inside the IMC. Thus, if the IMC is
thicker than the pulse length, a low-brightness region isobserved on the adventitia side of the IMC. Thereafter, theultrasound is strongly scattered/reflected at the interface
between the media and adventitia, and a high-brightness
region is observed at the adventitia.
The boundary depths fzb1 ðmÞg between the lumen
and intima are determined based on threshold processing,as shown in Figure 2b. First, the region fzj z1 zz2 g,
including both the lumen and IMC of the posterior wall,
was manually assigned. Thereafter, the shallowest depth
zb1 ðmÞ where the amplitude of the envelope is larger than
the threshold th is determined as the boundary depth as

Visualization of longitudinal displacement at IMC  S. MORI et al.

877

Fig. 1. (a) Schematic of measurement configuration for anatomic M-mode imaging and (b) the displacement (A) visualized in the anatomic M-mode imaging. (c) Schematic of measurement configuration for the carotid artery and (d) longitudinal displacement (A) visualized in the proposed lateral M-mode imaging.


zb1 ðmÞ ¼ min arg frðz; m; 0Þthg ; ðm ¼ 0; . . . ; M  1Þ
z

z

ð1Þ

Fig. 2. (a) Schematic of the B-mode image of the posteriorwall. (b) Example of a set of depths, fzb1 ðmÞg and fzb2 ðmÞg, ofthe boundaries of the intimamedia complex (IMC).

where rðz; m; nÞ denotes the envelope of the RF signal on
the mth beam at the nth frame, and M denotes the total
number of ultrasound beams. This threshold processing
was applied to each ultrasound beam independently for
the 0th frame.
The boundary depths fzb2 ðmÞg are set at the local
minimum depths of the envelope inside the IMC, as
shown in Figure 2a and 2b, to exclude the large signals
from the adventitia that exhibits different movementfrom the IMC (Cinthio et al. 2006). However, theenvelope at the depth of the local minimum is easily
affected by background noise. To increase thesignal-to-noise ratio, the envelopes measured by M
ultrasound beams were averaged assuming that the
thickness of the IMC was almost the same inthe longitudinal direction in the early stage of arteriosclerosis.

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In the actual case, the ultrasound probe surface canincline in the longitudinal direction of the carotid artery,as shown in Figure 3a and 3b. Thus, the inclination iscorrected by zb1 ðmÞ by introducing z0 ¼ z  zb1 ðmÞ; asshown in Figure 3b and 3c. The corrected envelope signal r0 ðz0 ; mÞ on the mth beam is defined at the 0th frameasr0 ðz0 ; mÞ ¼ rðz0 þ zb1 ðmÞ; m; 0Þ:
Subsequently, the corrected envelope
fr0 ðz0 ; mÞg are averaged (Fig. 3c, 3d), asr 0 ðz0 Þ ¼

X
1 M1
r0 ðz0 ; mÞ:
M m¼0

ð2Þ
signals

ð3Þ

The thickness of the IMC region, DhIMC , is thereafter
determined as the shallowest local minimum depth ofr0 ðz0 Þ as
DhIMC ¼ min
farg fr0 ðz0 Þ < r0 ðz0  dzÞ \ r0 ðz0 Þ < r0 ðz0 þ dzÞgg;
0
z

z0

ð4Þ
where dz denotes the sampling interval in the depth
direction. Finally, the depth zb2 ðmÞ is determined aszb2 ðmÞ ¼ zb1 ðmÞ þ DhIMC ; ðm ¼ 0; . . . ; M  1Þ:ð5Þ

Thus, the depths fzb1 ðmÞg and fzb2 ðmÞg were determinedfor each beam m as shown in Figure 3e.
Using the depths fzb1 ðmÞg and fzb2 ðmÞg, the depthsof the target line for lateral M-mode imaging at the 0thframe, fz0 ðmÞg, were defined, as shown in Figure 3e:ð6Þ

Fig. 4. Example of the longitudinal movement visualization of
the intimamedia complex (IMC) on the lateral M-mode. (a,b) B-mode images in the (a) 0th and (b) 80th frames. (c) Electrocardiogram (ECG). (d, e) Lateral M-mode: proposed visualized images of the longitudinal movement of the IMC with theuse of the (d) amplitude of the envelope and (e) amplitude ofthe differentiated envelope.

Principle: Lateral M-mode imaging
The objective is to visualize the longitudinal displacement (A) of the IMC, as shown in Figure 1c and1d; therefore, the target line for lateral M-mode imaging
at the 0th frame is set at depths fz0 ðmÞg along the longitudinal direction of the IMC by eqn (6). Because the
IMC moves in both the longitudinal and radial directions

z0 ðmÞ ¼

zb1 ðmÞ þ zb2 ðmÞ:
2Fig. 3. Schematic of the set of the depths of the target line at the 0th frame, fz0 ðmÞg, for lateral M-mode imaging.

Visualization of longitudinal displacement at IMC  S. MORI et al.

by pulsation, as shown in Figure 1c, the position of thetarget line is corrected frame-by-frame along the radialdisplacement (B) asznþ1 ðmÞ ¼ z0 ðmÞ þn
1 X
vd ðk; mÞ;FR k¼0ð8Þ

and the use of a differentiated envelope between consecutive ultrasound beams to emphasize the difference inamplitude in the longitudinal direction, as
sn ðz; mÞ ¼ rðz; m þ 1; nÞ  rðz; m; nÞ:

downward directions, which correspond to the rightward
and leftward directions in the B-mode image, that is, themovements toward the heart and head sides, respectively.

ð7Þ

where zn ðmÞ denotes the depth of the target line on themth beam at the nth frame, FR denotes the frame rate
and v^d ðn; mÞ denotes the velocity in the radial direction
between the nth and ðn þ 1Þth frames estimated on themth beam, which was obtained using a multifrequencyphased tracking method (Obara et al. 2021) with a window length of DhIMC . When zn ðmÞ is not the integral
multiple of sampling interval dz, it is rounded off to be
the closest integral multiple of dz.
Subsequently, the signals fsn ðzn ðmÞ; mÞg on the target
line fzn ðmÞg in the nth frame are visualized as the lateral Mmode, where we compare the use of two different types ofsignals for sn ðz; mÞ: the conventional use of an envelope, assn ðz; mÞ ¼ rðz; m; nÞ;

879

ð9Þ

Finally, the amplitudes of the signals
fsn ðzn ðmÞ; mÞg on the target line fzn ðmÞg are converted
to 8-bit grayscale pixel values fIL ðn; mÞg 2 ½0; 255 as
8
0
>
>
<
sn ðzn ðmÞ; mÞ  ar1
IL ðn; mÞ ¼
b 255 ¢
þ 0:5 c ;>ar2  ar1
>
:
255
ð10Þ
where b ¢ c denotes an operation of the floor function
and ½ar1 ; ar2  denotes the visualized amplitude range ofthe signal sn ðzn ðmÞ; mÞ. The pixel values IL ðn; mÞ of 0
and 255 indicate black and white, respectively, andfIL ðn; mÞg is visualized as a lateral M-mode image withframe n on the horizontal axis and beam number m on
the perpendicular axis.
Figure 4 shows an example of lateral M-mode
imaging. Figure 4a and 4b show the depths of the target
line at the 0th frame, fz0 ðmÞg, and at the 80th frame,
fz80 ðmÞg, respectively. The target line moved in theradial direction, as shown in Figure 4a and 4b. Figure 4cshows the electrocardiogram (ECG) waveform. Figure
4d and 4e show the lateral M-mode images obtainedusing eqns (8) and (9), respectively. In Figure 4d and 4e,½ar1 ; ar2  was set as ½0; 2000 and ½500; 500, respectively. The longitudinal movement of the IMC is visualized as a change in equal pixel values in the upward andMeasurement configuration
The right common carotid arteries in three healthy
young volunteers, namely, A, B and C in their earlytwenties, and the older healthy volunteer D in his early
fifties (all volunteers were male with no obesity), were
measured using an ultrasound diagnostic apparatus. The
in vivo measurements used in this study were approvedby the ethics committee of the Graduate School of Engineering at Tohoku University (No. 19A-5). All the participants agreed to participate in the study.
A linear probe (UST-5410, Hitachi-Aloka-Medical
Ltd., Tokyo, Japan) connected to an ultrasound diagnostic apparatus (SSD-6500, Hitachi-Aloka-Medical Ltd.)was used. The diagnostic apparatus was customized to
output the raw beamformed RF signals. The acquired
raw beamformed RF signals were loaded and analyzed
offline using a program developed by our group that was
operated using MATLAB R2020b (The MathWorks
Inc., Natick, MA, USA). Center frequency, sampling frequency and beam intervals of 7.5 MHz, 40 MHz and
150 mm, respectively, were used. The number of ultrasound beams, M, was set as 47. The frame rate was set at
286 Hz, at which the maximum instantaneous velocity
of approximately 14 mm/s can be measured without alisn ðzn ðmÞ; mÞ < ar1
ar1 sn ðzn ðmÞ; mÞ < ar2
sn ðzn ðmÞ; mÞar2
asing, under the condition the transmitted frequency was
7.5 MHz (the wavelength is approximately 0:2 mm),which was empirically sufficient for measuring the radial
velocity of the carotid artery wall. The electrocardiogram (ECG) was simultaneously measured for lead II
using the three-point lead method.
Estimation of longitudinal displacement of the IMC by aconventional block-matching method
The proposed lateral M-mode was applied to validate the estimated longitudinal movement of the IMC
using a conventional block-matching method.
In this study, the conventional block-matching
method based on normalized cross-correlation (Golemati
et al. 2003) was used to estimate the longitudinal displacement between consecutive frames, Dxn , of the IMC
by maximizing the normalized cross-correlation Cn
between consecutive frames. The longitudinal position

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Ultrasound in Medicine & Biology

xn in the nth frame is tracked asxnþ1 ¼ x0 þ

n
X

Dxk ;

ð11Þ

k¼0

where x0 denotes the center position of the correlation
kernel at the 0th frame (time of the first R-wave).
Because the lateral sampling interval dx, which was
150 mm in this study, is larger than the longitudinal displacement of the IMC between frames (Kitamura et al.
2012), the normalized cross-correlation function Cn wasinterpolated using reconstructive interpolation (Cespedes
et al. 1995) such that the interpolated sampling intervals
became approximately 1 mm in both the depth and lateral directions.
When updating the depth of the correlation kernel
from the nth frame to the ðn þ 1Þth frame, the tracked
depth zn ðmÞ obtained with the multifrequency phased
tracking method in eqn (7) was used instead of the
tracked depth obtained with the block-matching method
because the phase of the RF signal can be effectively
used in the depth direction.
The differentiated envelope between the consecutive ultrasound beams defined in eqn (9) was used in theblock-matching method to emphasize the difference inthe envelope in the longitudinal direction. The width ofthe correlation kernel was empirically determined as
2.4 mm (17 beams). The center depth of the correlation
kernel on the mth beam was set at the depth of the target
line zn ðmÞ. The height of the correlation kernel was set
to DhIMC which was determined by eqn (4); 0.35 mm forparticipants A, B and D, and 0.39 mm for participant C.
The height of the correlation kernel was fixed throughout
the cardiac cycle.
Figure 5a and 5b show examples of the conventional B-mode image and the image of the differentiatedenvelope between consecutive beams, respectively, atthe 0th frame (the time of the first R-wave). The red parallelograms in Figure 5a and 5b show an example of theposition of the correlation kernel at the 0th frame for theblock-matching method. Although the brightness of the
IMC was almost homogeneous in the longitudinal direction, as shown in Figure 5a, the pattern of positive values(high brightness) and negative values (low brightness)
observed in Figure 5b can be effectively used in theblock-matching method.
Figure 5c and 5d show the spatial distributions of
the normalized cross-correlation Cn between the 0th and1st frames, calculated for the envelope rðz; m; nÞ and forthe differentiated envelope rðz; m þ 1; nÞ  rðz; m; nÞ,respectively. As shown in Figure 5c, large correlation
values were observed along the longitudinal direction;
therefore, estimating the displacement of the IMC may
become unstable. In contrast, in Figure 5d, the spatial

Volume 49, Number 3, 2023

distribution of the correlation value changes significantly, and its large value is concentrated at a single
position. Figure 5e shows the tracking results for the correlation kernel set shown in Figure 5a and 5b. The results
were superimposed onto a lateral M-mode image.
The blue and red lines represent the results usingenvelope rðz; m; nÞ and differentiated envelope
rðz; m þ 1; nÞ  rðz; m; nÞ, respectively, in the blockmatching method. In the result obtained using the envelope (blue), the tracked position gradually deviated in
the heart direction compared with the trajectory observedin the lateral M-mode image. These examples indicatethat the use of a differentiated envelope is superior to thesimple use of an envelope for estimating the longitudinal
displacement of the IMC using the correlation-based
block-matching method.
Evaluation of validity of tracking results using lateral Mmode image
We evaluated the validity of the estimated longitudinal displacement using the block-matching method bycomparing the result with the trajectory observed in thelateral M-mode image. When the estimated displacement
corresponds to the trajectory on the lateral M-mode
image, the pixel values of the lateral M-mode image
along the estimated displacement become constantbecause the same point in the IMC is tracked throughout
the cardiac cycle.
Thus, we evaluated the standard deviation SDðx0 Þof the pixel values of the lateral M-mode image along
the estimated longitudinal position xn , asSDðx0 Þ ¼

vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
u N 1 




2
u1 X
xn
xn
t
IL;ip n; b
þ 0:5 c  En IL;ip n; b
þ 0:5 c
;
N n¼0
dxip
dxip

ð12Þ
where En ½ ¢  denotes the average operation for n ¼ 0; 1;⋯; N  1; xn denotes the estimated longitudinal positionat the nth frame, obtained using eqn (11), and x0 denotes
the lateral position of the correlation kernel for blockmatching in the 0th frame; IL;ip ðn; mip Þ denotes the interpolated lateral M-mode image of IL ðn; mÞ in eqn (10),which was interpolated along the m-direction (i.e., theperpendicular direction of the lateral M-mode image),
mip denotes the interpolated beam number and dxip
denotes the interpolated lateral sampling interval of the
B-mode image (i.e., the perpendicular sampling intervalof the lateral M-mode image). dxip was set as 1 mm,
which is the same as the interpolation for the correlation
function Cn in the block-matching method. Here, similar
to the block-matching method, interpolation along them-direction was used because the instantaneous

Visualization of longitudinal displacement at IMC  S. MORI et al.

881

Fig. 5. (a) Conventional B-mode image and (b) image of the differentiated envelope between consecutive ultrasoundbeams at the 0th frame (time of R-wave) for participant A. (c, d) Normalized cross-correlations between the 0th and 1st
frames where the correlation kernel was set as a red parallelogram on (a) and (b), respectively. (e) Estimated results of
the longitudinal displacement of the intimamedia complex (IMC) by the block-matching method, superimposed on thelateral M-mode image. The result using the differentiated envelope in the block-matching method is plotted as a blueline and the result using the simple envelope is plotted as a red line.

displacement Dxn between consecutive frames was
smaller than the sampling interval of dx ¼ 150 mm. The
small value of SDðx0 Þ indicates that the difference in the
pixel values of the lateral M-mode image along the estimated longitudinal displacement is small; that is, theestimated displacement by the block-matching method
corresponds to the trajectory observed in the lateral Mmode image obtained using an approach different fromthe block-matching method.
RESULTS
Lateral M-mode imaging
Figure 6ad show conventional B-mode images forparticipants AD, respectively. The red and blue solidlines represent the boundary depths of the IMC region,
fzb1 ðmÞg and fzb2 ðmÞg, determined using eqns (1) and(5), respectively, and the black dashed line represents
the depths of the target line at the 0th frame, fz0 ðmÞg,determined using eqn (6). For all participants, fzb1 ðmÞgand fzb2 ðmÞg were determined to include only the IMC,
and the target line at the 0th frame was precisely
assigned to the depth of the IMC.
Figure 7iiii show the ECG, lateral M-mode
images obtained using the amplitude of the envelope ineqn (8) and the lateral M-mode image using the amplitude of the differentiated envelope in eqn (9), respectively. Figure 7ad show the results for participantsAD, respectively. Lateral M-mode images of two consecutive cardiac cycles are shown. As shown in the882

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Fig. 6. Detected boundary depths fzb1 ðmÞg (red solid line) and fzb2 ðmÞg (blue solid line) and determined depths of thetarget line at the 0th frame, fz0 ðmÞg (black dashed line). (ad) Participants AD, respectively.

Fig. 7. (i) Electrocardiogram (ECG). (ii) Lateral M-mode images with the use of the amplitude of the envelope. (iii) Lateral M-mode images with the use of the amplitude of the differentiated envelope. (ad) Participants AD, respectively.

Visualization of longitudinal displacement at IMC  S. MORI et al.

longitudinal movement in the lateral M-mode, the IMC
moved to the heart side and thereafter returned to thehead side for all participants.
In Figure 7ii, the lateral M-mode exhibits a globalchange in brightness along the time direction. For
instance, in Figure 7c-ii, the amplitudes of the envelope became large from 0.15 to 0.5 s, compared withthat from 0 to 0.15 s, regardless of the lateral positions. Moreover, as shown in Figure 7b-ii, the amplitude of the envelope significantly decreased in thesecond cardiac cycle. In contrast, the differentiatedenvelope in Figure 7iii exhibits only a brightnesschange along the longitudinal direction (perpendicular
direction in Figure 7iii), which reflects the longitudinal movement of the IMC. Thus, for the proposed lateral M-mode, a differentiated envelope was suitablefor observing the longitudinal movement of the IMC.
Validation for estimated 2-D displacements
To demonstrate the use of the proposed lateral Mmode imaging method, the results of the longitudinal
displacements estimated using the conventional blockmatching method were superimposed on the lateral Mmode image. Figure 8iiii show the ECG, the conventional M-mode image in the radial direction and the proposed lateral M-mode image, respectively. Figure 8adshow the results for participants AD, respectively. The
differentiated envelope in eqn (9) was used for lateral
M-mode imaging. The depth of the target line,zn ðm ¼ 24Þ, on the 24th beam (center beam) is plotted in
Figure 8ii using the yellow line. The longitudinal position xn tracked by the block-matching method for the differentiated envelope is plotted in Figure 8iii with red,green and blue lines. The different colors represent theresults for the different center positions of the correlation
kernel in the 0th frame (the time of the first R-wave) inthe block-matching method.
The depth of the target line (yellow line),zn ðm ¼ 24Þ, in Figure 8ii corresponds well to the trajectory observed in the conventional M-mode image.
Similarly, the tracked longitudinal positions xn (red,blue and green lines) in Figure 8iii correspond well to
the trajectories observed in the proposed lateral Mmode image for two consecutive cardiac cycles. Thus,
the precision of the estimated longitudinal displacements was qualitatively confirmed by comparing themwith the proposed lateral M-mode images.
To quantitatively evaluate the validity of the estimated longitudinal displacement by the block-matching method, the standard deviation SDðx0 Þ for the
pixel values in the lateral M-mode image was evaluated using eqn (12). The standard deviation SDDE ðx0 Þ
obtained for the longitudinal displacement estimatedusing the differentiated envelope rðz; m þ 1; nÞ  r

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ðz; m; nÞ and the SDE ðx0 Þ for the longitudinal displacement estimated using the simple envelope rðz; m; nÞ inthe block-matching method were compared. The maximum value among the results for three different initial
positions x0 of the correlation kernel was evaluated.
The maximum values obtained were 30 ðSDDE ðx0 ÞÞ
versus 39 ðSDE ðx0 ÞÞ for participant A, 30 versus 88 forparticipant B, 17 versus 24 for participant C and 20
versus 39 for participant D, where the upper limit of
the pixel value was 255, as defined by eqn (10). Thus,
for all participants, the standard deviation SDDE(x0)obtained for the longitudinal displacement estimatedusing the differentiated envelope was less than theSDE(x0) for the longitudinal displacement estimatedusing the envelope. Determining the threshold of SD
that guarantees the accuracy of the estimated displacement is part of our future study.
We observed the trajectory of the 2-D displacementfrom each of the three initial positions (xnx0, znz0) of
the IMC for four participants, as shown in Figure 8iv. In
Figure 8iv, the positions at the time of the first R-wave
are defined as ð0; 0Þ, those at the time of the second Rwave as circles and those at the time of the third R-wave
as squares. The trajectories in the first and second cardiac cycles are represented by solid and dotted lines,
respectively.
In Figure 8iv, the results are shown to follow asimilar trajectory between consecutive cardiac cycles,
although with subtle differences. Moreover, the trajectory returned to its original position ð0; 0Þ after one
cardiac cycle. The detailed 2-D trajectory differed byparticipant; however, the tendency of the trajectory
was similar, particularly for participants A and C: (I)first, the IMC moved mainly in a radial direction byvessel dilatation; (II) this was followed by movement
in a longitudinal direction toward the heart side; (III)thereafter the IMC moved mainly in a longitudinal
direction toward the head side (returning movement);and (IV) finally returned to its original position by
moving in a radial direction. This figure-of-eight pattern was also reported by Au et al. (2019), who measured it for young children under 10 y of age, although
the detailed trajectories were different from the present results in Figure 8iv. Note that the right direction
corresponds to the direction toward the head, and theupper direction corresponds to the deeper direction of
the B-mode image in the coordinates for the 2-D trajectory reported by Au et al. (2019). These orientations were opposite to the directions in Figure 8iv. For
participant B, a similar pattern was observed, although
it was not as pronounced as compared with those forparticipants A and C. For participant D in his early fifties, the figure-of-eight pattern was not observed, as
shown in Figure 8d-iv.

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Volume 49, Number 3, 2023

Fig. 8. (i) Electrocardiogram (ECG). (ii) Conventional M-mode image. (iii) Lateral M-mode image with the use of theamplitude of the differentiated envelope. (iv) Trajectories of 2-D displacements of the intimamedia complex. (ad)Participants AD, respectively. The estimated depth of the target line, zn (m ¼ 24), on the 24th beam (center beam) isrepresented by the yellow line in (ii). The longitudinal positions xn estimated by the conventional block-matching method
at the three points are superimposed in (iii).

Visualization of longitudinal displacement at IMC  S. MORI et al.

DISCUSSION
In this study, lateral M-mode imaging, which visualizes the longitudinal movement of the IMC, is proposed.
As shown in Figure 6, the boundary depths of the
IMC region, fzb1 ðmÞg and fzb2 ðmÞg, were precisely
determined to include only the IMC in all four healthy
participants. This procedure aims mainly to exclude
large signals from the adventitia because the movementof the adventitia differs from that of the IMC, as reported
by Cinthio et al. (2006). Hence, the inclusion of theentire IMC in the ROI was not necessary for this study.
Therefore, this method cannot guarantee whether thedetermined boundary is exactly the boundary between
the media and adventitia, although it can stably exclude
signals from the adventitia. Thus, when this method isapplied to other applications such as IMT measurements,
careful examination is required. The determination
method for the IMC region was also developed by othergroups, as summarized by Meiburger et al. (2022). A
simple threshold approach was used in the present study
to determine the boundary between the lumen andintima. The approach worked well for the measurements
conducted in this study; however, the application of amore robust detection method proposed by other groups
will improve the robustness of lateral M-mode imaging
and displacement estimation by the block-matching
method, particularly for less echogenic data in older and/or diseased participants. The robustness of the IMC
boundary detection method may affect the robustness of
the lateral M-mode imaging and longitudinal displacement estimation by the block-matching method; therefore, an evaluation of the robustness of each method is a
topic for future work.
For the lateral M-mode, which visualizes the longitudinal movement of the IMC using eqn (10), a clear andsharp image was obtained by introducing a differentiatedenvelope between consecutive beams using eqn (9), as
shown in Figure 7iii. There are several possible reasons forthis finding. First, the difference in brightness in the longitudinal direction is emphasized by differentiating the envelopes between consecutive beams. Second, the global
brightness change in the time direction (i.e., the frame
direction) was observed using eqn (8) (Fig. 7ii), but notwith eqn (9) (Fig. 7iii), as described under Results section.
The cause of this global brightness change in time direction
remains unclear. However, this global brightness change
appeared only in the time direction and not in the longitudinal direction, and was suppressed by differentiating theenvelopes between consecutive beams (i.e., differentiatingin the longitudinal direction). Thus, only the brightnesschange caused by the longitudinal displacement of the
IMC was emphasized, as shown in Figure 7iii.

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For lateral M-mode imaging, only a 1-D phasebased estimator for the radial displacement was used.
We discuss the computational capacity of the 1-D phasebased estimator used for lateral M-mode imaging andthe 2-D block-matching method used for longitudinal
displacement estimation. It is difficult to compare thedetailed computational capacity because it depends on
the algorithm used and the use/non-use of parallel processing. Therefore, we compared the dominant order ofthe number of multiplied operations used in eachmethod.
In the 1-D multifrequency-phased velocity estimator (Obara et al. 2021), the dominant factor affecting
computational capacity is the Fourier transform. Therefore, the dominant order of the number of multiplied
operations is L2d (Ld is the window length in the radial
direction) when a simple discrete Fourier transform isused.
In the 2-D block-matching method used for longitudinal displacement estimation, the dominant procedure
affecting the computational capacity is the interpolationof the 2-D cross-correlation function Cn , which is
required to estimate the sub-pixel displacement. In thisstudy, Cn was interpolated by factors of 20 in the depth
direction and 150 in the lateral direction, to ensure thatthe interpolated sampling intervals were approximately
1 mm. The dominant order of the number of multiplied
operations in the procedure for interpolation in the time
domain is ð20Ld  Lw Þ  L2d (interpolation in the depth
direction) þ ð20Ld  150Lw Þ  L2w (interpolation in thelateral direction).
In this study, Ld was 19 for participants A, B and D,
and 21 for participant C; and Lw was 17 for all participants. Thus, under the present measurement condition,
the 1-D velocity estimator used for lateral M-mode
imaging can reduce the dominant order of the number ofmultiplied operations from 108 (or 107 when the interpolation is conducted in the frequency domain with the fast
Fourier transform) to 102 , for each lateral position andframe, compared with the 2-D block-matching method
used for the longitudinal displacement estimator.
By comparing the estimated longitudinal displacements of the IMC with the lateral M-mode image, we
confirmed that the longitudinal displacement estimatedby the block-matching method for the differentiatedenvelope corresponded well to the trajectory observed in
the lateral M-mode image compared with the result using
the simple envelope in the block-matching method. The
lateral M-mode image is obtained using an approach different from the longitudinal displacement estimator(block-matching method in this study); that is, the lateral
M-mode imaging is not affected by the longitudinal displacement estimator used. Thus, the lateral M-mode
image may be effective in validating the longitudinal

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displacement estimator and may contribute to the development of an accurate estimation method for the longitudinal movement of the IMC.
In the block-matching method used in this study, theheight of the window was fixed throughout the cardiac
cycle. However, Rafati et al. (2019) reported that the IMTof the common carotid artery changes by a maximum of
approximately 125 mm in a cardiac cycle, which is achange of approximately 10%. Thus, adaptively changing
the window height may improve tracking accuracy. Development of a more accurate method for estimating the longitudinal displacement of IMC is a future challenge.
T
edPTag he trajectories of the 2-D displacements in Figure 8(a-iv to c-iv) for young healthy adults A, B and C in theirearly twenties differed by participant, although the shapeof the trajectory exhibited a similar tendency. Differences in the measurement conditions, such as the pushingforce of the probe, may affect the movement of the
carotid artery wall. The trajectory of 2-D displacements
for young healthy adults A, B and C in their early twenties exhibit the figure-of-eight pattern, which was also
reported by Au et al. (2019) measured for children younger than 10 y of age. However, there were some differences between the trajectory waveforms obtained in thisstudy and those reported by Au et al. (2019). Moreover,for older healthy adult D in his early fifties, the figureof-eight pattern was not observed, as shown in
Figure 8d-iv. As reported by Au et al. (2017), the waveforms of radial and longitudinal displacements of the
carotid artery wall differ based on age. This is one of theprospective reasons for the aforementioned differencesin the trajectories of the 2-D displacements. As the number of participants was limited in the present study, adetailed analysis of a large number of participants in different age groups, including the robustness evaluation
for less echogenic data, is necessary for our future study.
In this study, we applied the proposed method only
to the right common carotid artery; therefore, in futurestudies, we will examine the applicability of the method
to other targets, such as the left common carotid arteryand the right and left carotid sinuses.
In the present study, raw RF signals were used forlateral M-mode imaging; therefore, the proposed methodneeds to be implemented in the diagnostic apparatus by
manufacturers as a new application for clinical use. To
expand the application of the proposed lateral M-mode
imaging, we will examine the method applicable to compressed data that can be acquired from the commerciallyused diagnostic apparatus by clinicians themselves.
CONCLUSIONSIn this study, the “lateral M-mode” method is proposed for visualizing the longitudinal movement of theVolume 49, Number 3, 2023

IMC. The lateral M-mode can be used for validation of
the longitudinal displacement estimator. Moreover, we
can observe the longitudinal movement of the IMC only
from the lateral M-mode image, without estimating thelongitudinal displacement. For lateral M-mode imaging,
only a 1-D phase-based estimator with a low computational capacity is required; therefore, it may be implementable in clinical applications. As the conventional
M-mode sequence plays an important role in evaluationof the dynamics of various tissues, the “lateral M-mode”
proposed for visualization of the longitudinal movementof the IMC will contribute to the detailed understandingof vascular dynamics and the development of diagnostic
methods for vascular diseases.
DATA AVAILABILITY STATEMENT
The authors do not have permission to share data.
Acknowledgments—This study was supported in part by Japan Society
for the Promotion of Science KAKENHI Grants 19KK0100 and
21K14166.
Conflict of interest disclosure—The authors declare that they have nocompeting interests.

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