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ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 53, no. 11, november 2006

Modiﬁcation of the Phased-Tracking Method
for Reduction of Artifacts in Estimated Artery
Wall Deformation
Hideyuki Hasegawa, Member, IEEE, and Hiroshi Kanai, Member, IEEE
Abstract—Noninvasive measurement of mechanical properties, such as elasticity, of the arterial wall, is useful for
diagnosis of atherosclerosis. For assessment of mechanicalproperties, it is necessary to measure the deformation of
the arterial wall. In this study, a modiﬁcation of the previously proposed phased-tracking method was conducted to
improve measurement of the small change in thickness (deformation) of the arterial wall due to the heartbeat. In ourprevious method, a set of two points along an ultrasonicbeam was initially assigned, and the change in thickness of
the layer between these two points during an entire cardiac
cycle was estimated. In motion estimation with ultrasound,the motion of an interface or a scatterer, which generates
an echo, can be obtained by estimating the change in timedelay of the echo. For example, in the case of a carotid
artery of a healthy subject, there are only two dominantechoes from the lumen-intima and media-adventitia interfaces. Thus, only the displacements of the lumen-intima andmedia-adventitia interfaces can be estimated, which meansthat ultrasound can estimate only the change in distance(thickness) between these two interfaces. However, even inthis case, our previous method gives diﬀerent estimates of
the change in thickness, depending on the depths (positionsin the arterial radial direction) of the two initially assigned
points. In this study, modiﬁcations of the previous method
in terms of the strategy for assignment of layers and the required thickness of an assigned layer were made to reducesuch an artiﬁcial spatial variation in the estimated changes
in thickness. Using the proposed method, errors in esti24.1%
mated changes in thickness were reduced from 21.2
to 0.19
0.04% (meanstandard deviation) in simulation
experiments. As in the case of the simulation experiments,
the spatial variation in estimated changes in thickness also
was reduced in in vivo experiments in a carotid artery of ahealthy subject and in vitro experiments using two excised,diseased arteries.

I. Introduction
oninvasive measurement of mechanical properties of
the arterial wall, such as elasticity, is useful for diagnosing atherosclerosis because there are signiﬁcant diﬀerences between the elastic moduli of normal arterial walls
and those aﬀected by atherosclerosis [1], [2].
For assessment of mechanical properties, various methods have been proposed to measure the displacement of thearterial wall. Elasticity based on estimation of the pulse

N

Manuscript received October 22, 2005; accepted May 28, 2006.
The authors are with the Department of Electronic Engineering,
Graduate School of Engineering, Tohoku University, Sendai 9808579, Japan (e-mail: hasegawa@us.ecei.tohoku.ac.jp).
Digital Object Identiﬁer 10.1109/TUFFC.2006.145

wave velocity (PWV) [3]–[6] and the homogeneity of distensibility [7], which is evaluated by the change in diameter obtained from displacements of near and far walls, canbe noninvasively evaluated by measuring displacements at
multiple points in the axial direction of the artery. Of
course, measurement of the change in diameter at one
point is widely used for assessment of mechanical properties of the arterial wall [8]–[10]. In such case, however,
the arterial wall must be assumed to be an isotropic, cylindrical shell with a uniform wall thickness.
In addition to the displacement distribution in the axial direction of the artery, the distribution in the radial
direction of the arterial wall has been measured with intravascular ultrasonography (IVUS) [11], [12]. The elasticity distribution of coronary atherosclerotic plaque has
been obtained [12] based on the measurement of the radial strain [11]. Furthermore, model-based methods havebeen proposed for improving the strain estimation [13].
In those studies, such a measured elasticity distribution
was compared with the pathological image and suggested
the potential for tissue characterization of atherosclerotic
plaque by measurement of its elasticity.
As a transcutaneous approach, the displacement andstrain around carotid atherosclerotic plaque have beenmeasured using tissue Doppler imaging [14]. The inhomogeneity of displacements measured upstream and downstream of atherosclerotic plaque suggested that motion of
the arterial wall has potential for use in the evaluation ofplaque vulnerability. Furthermore, in recent years, someresearch studies on noninvasive vascular elastography havebeen conducted [15], [16].
We previously developed a method, namely, the phasedtracking method, for measuring small vibrations on theheart or arterial wall with transcutaneous ultrasound [17],[18]. For some years now, we have been measuring thedisplacement and change in thickness of the arterial wallcaused by the heartbeat using this method [19]–[21]. Elasticity images of the human carotid artery have been obtained by the measured displacement distribution, and thepotential for transcutaneous tissue characterization has
been shown by classifying the elasticity images using theelasticity reference data obtained by in vitro experiments[22]–[24].
Although the noninvasive methods for measuring theintima-media thickness [25] and lumen diameter [26] basedon the automated image segmentation are useful for diagnosis of the morphology of the arterial wall and atheroscle-

c 2006 IEEE
0885–3010/$20.00 hasegawa and kanai: modification of phased-tracking method and artery wall deformation

Fig. 1. Schematic of measurement.

rotic plaque, the measurements of mechanical properties—
including our method—also are important because myocardial infarction and stroke are mainly caused by therupture of atherosclerotic plaque [27], [28].
In the phased-tracking method, the small deformationof the arterial wall can be detected based on precise estimation of the velocity of the arterial wall. The velocity is
estimated by the phase shift of echoes that corresponds tothe change in the time delay for two-way propagation ofultrasound between an ultrasonic probe and the arterial
wall. The phase shift can be estimated at each frequency
within the frequency bandwidth of an echo. However, werecently revealed that the estimated velocity is biased unless the phase shift is estimated at the center frequency ofan echo [29]. Although this error is not so large during aframe interval, the estimated velocity must be integrated
with respect to time for tracking the position of the arterial wall. Therefore, this error becomes signiﬁcant due toaccumulation resulting from temporal integration.
In this study, a source of error in estimation of the deformation of the arterial wall was investigated. In our previous phased-tracking method [20], [21], [23], a set of two
points was assigned along an ultrasonic beam as shown in
Fig. 1, and the change in thickness of the layer between
these two points was estimated. Furthermore, by sliding
the position of the layer along an ultrasonic beam by intervals of the sampled points, the spatial distribution ofchanges in thickness along the ultrasonic beam was obtained.
In such a motion estimation with ultrasound, the motion of an interface or a scatterer, which generates anecho, can be obtained by estimating the change in timedelay of the echo. For example, in the case of a carotid
artery of a healthy subject, there are only two dominantechoes from the lumen-intima and media-adventitia in-

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terfaces [30]. Thus, only the displacements of the lumenintima and media-adventitia interfaces can be estimated,which means that ultrasound can estimate only the change
in distance (thickness) between these two interfaces. However, even in such a case, the previous phased-tracking
method gives diﬀerent estimates of the change in thickness, depending on the depths (positions in the arterial
radial direction) of the two initially assigned points. In
this study, modiﬁcations of the previous method in termsof the strategy for assignment of layers and the required
thickness of a layer were made to reduce such an artiﬁcial
spatial variation in the estimated changes in thickness.
In the estimation of the change in thickness using thecorrelation estimator, the thickness of an assigned layer islarger than the interval of sampled points, and the layer
is slid by the interval of sampled points. Therefore, several layers with respective correlation estimators overlap
at each depth. In this study, correlation estimators of layers, which overlap at a certain depth, were compounded toobtain the change in thickness at that depth. Although theangle of the ultrasonic beam was not changed in this study,
the concept of spatial compounding already has been applied to magnitudes of echoes, which are obtained by scanning each point in the region of interest with ultrasonicbeams having diﬀerent beam angles, to improve B-mode
images [31].

II. Methods
A. Previously Proposed Phased-Tracking Method for
Imaging Radial Deformation of Arterial WallRadio frequency (RF) pulses with a center frequencyof f0 are transmitted with a time interval T from an ultrasonic transducer, and the echo reﬂected by an interface or a scatterer is received by the same transducer asshown in Fig. 2. The propagation delay, τ1 (n), between thetransducer and the reﬂector (interface or scatterer) at nth transmission (frame) depends on the sound speed, c0 ,and the distance d1 (n) between the transducer and thereﬂector:
2d1 (n)c0(n = 1, 2, · · · , N ; N : number of frames).

τ1 (n) =(1)

Phase θ1 (n) of a received echo is expressed by θ1 (n) =2πf0 τ1 (n) at the center frequency, f0 . Therefore, distances
d1 (n) and d1 (n + 1) between the ultrasonic transducer andthe reﬂector in n-th and (n + 1)-th frames are given by:c0 τ1 (n)c0=
· θ1 (n),2
4πf0
c0 τ1 (n + 1)
c0
d1 (n + 1) ==· θ1 (n + 1).
2
4πf0
d1 (n) =(2)(3)

The average velocity of the reﬂector during a frame interval, T , is deﬁned by v1 (n) = {d1 (n + 1) − d1 (n)}/T .

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ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 53, no. 11, november 2006

1 (n) =
ej∆θ


K/2

z ∗ (n; x1 (n) + k · ∆x) · z(n + 1; x1 (n) + k · ∆x)k=−K/2



 K/2

 

∗


z
(n;
x
(n)
+
k
·
∆x)
·
z(n
+
1;
x
(n)
+
k
·
∆x)
1
1


k=−K/2
= r1 (n),Fig. 2. Estimation of the change in thickness of the arterial wall by
the previously proposed phased-tracking method. (MT : total numberof assigned combinations, ML : number of sampled points between
two points of an assigned combination, T : frame interval, ∆x: spacingof sampled points, d1 (n) and d1 (n): depths of the lumen-intima andmedia-adventitia interfaces in n-th frame, xm (n) and xm (n): m-th (n): velocities
combination of two points in n-th frame, vm (n) and vm
at xm (n) and xm (n), respectively, ∆h(n, x): change in thickness at
depth x in n-th frame).

Thus, v1 (n) can be estimated from phase shift ∆θ1 (n) =θ1 (n + 1) − θ1 (n) of echoes as follows:
d1 (n + 1) − d1 (n)T
c0 (τ1 (n + 1) − τ1 (n))
=
2T
c0
=
· ∆θ1 (n).
4πf0 Tv1 (n) =(4)

To obtain phase θ1 (n) of an RF echo, the quadrature
demodulation at the center frequency, f0 , is applied tosampled RF echoes, and the sampled complex demodulated signal, z(n; x), is obtained along an ultrasonic beam(x-axis).
As shown in Fig. 2, by referring to an M-mode image, initial depth x1 (1) ≈ d1 (1) is manually assigned
as the position of the reﬂector at the ﬁrst frame. Initial depth x1 (1) usually does not exactly correspond tod1 (1) due to the manual assignment. However, phase shift∆θ1 (n) can be estimated at x1 (n) because the ultrasonicpulse used has a ﬁnite-pulse duration as shown in Fig. 2.
When x1 (1) is within the duration of the echo from d1 (1),phase ∠z(n; x1 (n)) of the complex demodulated signal,z(n; x1 (n)), at depth x1 (n) corresponds to θ1 (n):
θ1 (n) = ∠z(n; x1 (n)).

(5)

Thus, phase shift ∆θ1 (n) = θ1 (n + 1) − θ1 (n) between
two consecutive frames is estimated by the well-known autocorrelation function calculated as follows [17]:(6)

where ∆x is the interval of the sampled demodulated signal in the depth direction; ∗ and  represent the complex
conjugate and the estimate. In this study, the number ofsampled points, K, used for calculation of the correlation
function is determined by the width at −20 dB of the maximum magnitude of the quadrature demodulated signal of
the ultrasonic pulse. From the estimated correlation function r1 (n) obtained by (6), average velocity v1 (n) during
the frame interval, T , is obtained as follows:v1 (n) =c0
1 (n) = c0 · ∠r1 (n),· ∆θ
4πf0 T
4πf0 T(7)

where ∠r1 (n) represents the phase of the complex correlation function r1 (n).
In the estimation of the phase shift by (6), instantaneous position x1 (n) of the assigned point is tracked byaccumulation of displacement v1 (n) · T during a frame interval, T , as follows:
x1 (n) + v1 (n) · T.
x
1 (n + 1) = (8)When there are two reﬂectors (interface or scatterer) at
diﬀerent depths of d1 (n) and d1 (n), the change in thickness of the layer between these two reﬂectors is obtained asfollows: By referring to an M-mode image, initial position
x1 (1) ≈ d1 (1) is manually assigned at the ﬁrst frame as the
position of the lumen-intima interface. Then, as shown in
Fig. 2, another point, x1 (1) = x1 (1) + ML · ∆x, is automatically assigned at certain distance, ML ·∆x, from x1 (1)along the same ultrasonic beam. When x1 (1) corresponds
to the position of the echo from another reﬂector at d1 (1),the motion of the reﬂector can be estimated.
Then, velocities v1 (n) and v1 (n) of these assigned points
are obtained by tracking their instantaneous positions
x1 (n) and x1 (n) as described above. In the previously
proposed phased-tracking method, from estimated velocities v1 (n) and v1 (n), change in thickness ∆h(n; x) of thelayer between the two assigned points x1 (1) and x1 (1) =x1 (1) + ML · ∆x is obtained as the deformation at a depthof x1 (1) + ML · ∆x/2 as follows [23]: + 1; x1 (1) + ML · ∆x/2) =
∆h(n



∆h(n;
x1 (1) + ML · ∆x/2) + v (n) − v1 (n) · T,
1


∆h(1;
x1 (1) + ML · ∆x/2) = 0. (9)By sliding the combination of two points along the ultrasonic beam while keeping the distance between twohasegawa and kanai: modification of phased-tracking method and artery wall deformation

2053

The change in thickness between two reﬂectors at d1 (n)and d1 (n) then is obtained as follows. As shown by (2),phases θ1 (n) and θ1 (n) of echoes from these two reﬂectors
depend on d1 (n) and d1 (n). Thus, the phase diﬀerenceθh (n) = θ1 (n) − θ1 (n) depends on the distance h(n) =d1 (n)−d1 (n) (thickness of the layer) between two reﬂectors
as follows:
h(n) = d1 (n) − d1 (n)c0={θ (n) − θ1 (n)}4πf0 1c0· θh (n).
=
4πf0

(12)

Thus, as in the case of (4), the rate vh (n) of the change
in thickness of the layer between two reﬂectors is expressed
as follows:h(n + 1) − h(n)Tc0{θh (n + 1) − θh (n)}=4πf0 Tc0=· ∆θh (n).
4πf0 Tvh (n) =Fig. 3. Modiﬁed method for estimation of the change in thickness of
the arterial wall (MT : total number of assigned combinations, ML :number of sampled points between two points of an assigned combination, T : frame interval, ∆x: spacing of sampled points, d1 (n) andd1 (n): depths of the lumen-intima and media-adventitia interfaces
in n-th frame, xm (n) and xm (n): m-th combination of two points
in n-th frame, h(n): distance between the lumen-intima and mediaadventitia interfaces in n-th frame).

points constant (= ML · ∆x), the change in thickness∆h(n; xm (1) + ML · ∆x/2) at each depth is obtained asfollows: + 1; xm (1) + ML · ∆x/2) = ∆h(n;xm (1)∆h(n (n) − v
+ ML · ∆x/2) + v

(n)
· T,
m
m

∆h(1;
xm (1) + ML · ∆x/2) = 0,

(13)

As in the case of (5), when x1 (1) and x1 (1) assigned as shown in Fig. 3 are within the durations of
the echoes from d1 (1) and d1 (1), phase diﬀerence θh (n)can be expressed by phase ∠β(n; x1 (1), x1 (1)) of product β(n; x1 (1), x1 (1)) of complex demodulated signals,z(n; x1 (n))∗ and z(n; x1 (n)), as follows:θh (n) = θ1 (n) − θ1 (n) = ∠β(n; x1 (n), x1 (n)),(14)β(n; x1 (n), x1 (n)) = z(n; x1 (n)) · z ∗ (n; x1 (n)).
(15)

(10)

xm (1) = x1 (1) + m · ∆x, (m = 0, 1, 2, . . . , MT ),(11)
where MT is the manually determined number of times
that sliding occurs.
B. Modiﬁcation of the Phased-Tracking Method andCorrelation Estimator Compounding
In this section, the previously proposed phased-tracking
method is modiﬁed [21] with correlation estimator compounding.
As in Section II-A, by referring to an M-mode image, initial positions x1 (1) and x1 (1) of two points aremanually assigned at the ﬁrst frame as shown in Fig. 3(x1 (1) − x1 (1) = ML · ∆x). Then, instantaneous positions
x1 (n) and x1 (n) of these assigned points at the n-th frame
are tracked by the method described in Section II-A.

In this paper, correlation estimator rh (n; x) at depth x,
whose phase ∠rh (n; x) corresponds to θh (n + 1) − θh (n) =∆θh (n), is obtained by simply calculating the correlation
around the duration of echo as follows:rh (n; x1 (1) + i · ∆x) =

K/2




β n + 1; x1 (n)k=−K/2+ k · ∆x, x1 (n) + k · ∆x · β ∗ n; x1 (n)+ k · ∆x, x1 (n) + k · ∆x ,(i = 0, 1, 2, . . . , ML ) ,(16)

where the estimate in the right-hand side of (16) is used forcorrelation estimators rh (n; x) at all points between x1 (1)and x1 (1) in the modiﬁed method, whereas the change
in thickness between points x1 (1) and x1 (1) is used only
for the point that is midway between these two points, as
shown by (9) in the previous method.
As with (10), by sliding the combination of two points
along the ultrasonic beam while keeping the distance between the two points constant (= ML ·∆x), the correlation

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ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 53, no. 11, november 2006

estimator, rh,m (n; x), for each combination of two points,
xm (1) and xm (1), is obtained as follows:


K/2

r
h,m (n; xm (1) + i · ∆x) =
β n + 1; xm (n)k=−K/2+ k · ∆x, xm (n) + k · ∆x
· β ∗ n; xm (n)+ k · ∆x, xm (n) + k · ∆x ,(17)

xm (1) = x1 (1) + m · ∆x,m = 0, 1, 2, . . . , MT ; i = 0, 1, 2, . . . , ML ,(18)

where MT is the manually assigned number of times thatsliding occurs.
As shown in Fig. 3, MT assigned layers overlap eachother. Therefore, there are multiple estimates of rh (n; x)
at a depth x. The compounded correlation estimator,r̄h (n; x), at depth x then is obtained by simply averaging
overlapping correlation estimators as follows:1r̄h (n; xm (1)) =MO (xm (1))



m+MO (xm (1))

k=mrh,k (n; xm (1)),(19)

where MO (x) is the number of overlapping layers at
depth x.
The compounded rate, v̄h (n; x), of the change in thickness at depth x is obtained based on (13) as follows:v̄h (n; xm (1)) =c0· ∠r̄h (n; xm (1)).
4πf0 T(20)

The compounded change in thickness, ∆h̄(n; x), is obtained as follows:∆h̄(n + 1; xm (1)) = ∆h̄(n; xm (1)) + v¯h (n; xm (1)) × T.
(21)
The estimation of the velocity or rate of the change inthickness depends on the phase shift of received echoes,
and the velocity is larger than the rate of the change inthickness. Therefore, the required frame rate is determinedby the velocity of the arterial wall. The maximum velocityof the carotid arterial wall is typically about 10 mm/s.
Thus, when the ultrasound center frequency and speed ofsound are 7.5 MHz and 1540 m/s, respectively, the required
frame rate, F Rmin , is determined by substituting v1 (n) =10 mm/s and ∆θ1 (n) = π into (4) as follows:
F Rmin =4π × 7.5 × 106 × 10 × 10−3
= 195 Hz.
1540 × π(22)

In addition, the deformation estimate by the proposed
method depends on the time delay of an echo during twoway propagation between an ultrasonic probe and a reﬂector along an ultrasonic beam. Therefore, only the beamaxis component of the deformation can be measured by
the proposed method.

III. Drawbacks of Previously Proposed
Phased-Tracking Method
Fig. 4(a) shows a B-mode image of a carotid artery of
a 30-year-old, healthy male. The B-mode image was acquired using a 10 MHz linear-type ultrasonic probe of ultrasonic diagnostic equipment (SSD-6500, Aloka Co., Ltd.,Tokyo, Japan). Figs. 4(b) and (c) show RF echoes fromthe posterior wall along the white arrow in Fig. 4(a).
The region shown in Figs. 4(b) and (c) is indicated bya white dashed line in Fig. 4(a). In healthy subjects, there
are only two dominant echoes from the lumen-intima andmedia-adventitia interfaces [30]. In this study, as shownin Figs. 4(b) and (c), the intima-media thickness (IMT)
is deﬁned by the region between the rises of echoes fromthe lumen-intima and media-adventitia interfaces. In thisstudy, these rises were manually assigned by inspectinga B-mode or M-mode image. In motion estimation withultrasound, we can estimate the motion of a reﬂector (interface or scatterer) by analyzing its echo. Therefore, inthe case of a healthy subject, we can estimate only displacements of the lumen-intima and media-adventitia interfaces. Thus, only the change in thickness between theseinterfaces, which corresponds to the change in the entire intima-media thickness, can be obtained. As describedin [11], the deformation at a point in a cylindrical shellchanges in relation to its radial position, and such a change
depending on the radial position could be measured in [11]because there were many scatterers generating dominantechoes within the wall of the cylindrical phantom used.
As shown in Fig. 4(b), however, in cases of arteries ofhealthy subjects, there are only two dominant echoes fromtwo corresponding reﬂectors (lumen-intima and mediaadventitia interfaces). Under such a condition, althoughmultiple points can be assigned as shown in Fig. 2, eachassigned point gives the displacement of the lumen-intima
or media-adventitia interface. Therefore, only the deformation between two reﬂectors, which corresponds to thechange in thickness of the entire intima-media complex,
can be obtained; but the deformation at a point in thewall cannot be measured in such a situation.
However, changes in thickness obtained by the previously proposed phased-tracking method change depending
on depth (radial position in the wall), even when there are
only two reﬂectors. The reason for this is considered to be
as follows. At the ﬁrst frame, the lumen-intima and mediaadventitia interfaces are manually assigned as shown in
Fig. 4(b) by inspecting an M-mode image (or B-mode image). As shown in Fig. 4(b), there usually are discrepancies between the manually assigned interfaces and actualinterfaces due to the manual assignment based on an Mmode image. Then, the ﬁrst combination of the two points
x1 (1) and x1 (1) is assigned as shown in Fig. 4(b) to obtain the change in thickness at a certain depth, whichcorresponds to the manually assigned lumen-intima interface. The thickness of a layer, ML · ∆x, is assigned to be
the width at −6 dB of the maximum magnitude of thequadrature demodulated signal of the ultrasonic pulse inhasegawa and kanai: modification of phased-tracking method and artery wall deformation

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Fig. 5. Magnitude of the quadrature demodulated signal of the ultrasonic pulse used measured with a hydrophone placed in a watertank.

the previous phased-tracking method [23]. In a situationsuch as that shown in Fig. 4(b), x1 (1) and x1 (1) are assigned within the same echo from the lumen-intima interface. Therefore, both displacements, estimated at x1 (1)and x1 (1), correspond to that of the lumen-intima interface (high similarity of these two displacements). Thus, thechange in thickness (diﬀerence between these two displacements) is hardly detected. This is just an artifact due tothe ﬁnite duration of the ultrasonic pulse.
In the modiﬁed method in this study, x1 (1) and x1 (1)are assigned as shown in Fig. 4(c). To prevent x1 (1) frombeing assigned within the duration of the same echo fromthe lumen-intima interface, a larger thickness of a layer,
ML · ∆x, is necessary in comparison with the previous
method. Therefore, the required thickness of a layer, ML ·∆x, is investigated in Section IV-C.
In the simulation experiments in this study, the required
thickness of a layer, ML · ∆x, was investigated in relation
to the width of the magnitude of the quadrature demodulated signal of the ultrasonic pulse used. Fig. 5 shows
the magnitude of the demodulated signal of the ultrasonicpulse used measured with a hydrophone placed in a watertank. The hydrophone was placed at a distance of 20 mmfrom the surface of a linear-type probe, which corresponds
to the electric focal depth. The RF signal received by thehydrophone was acquired at a sampling frequency of 1 GHzwith a digital oscilloscope. Quadrature demodulation wasapplied to the sampled RF signal.

IV. Simulation Experiments

Fig. 4. (a) B-mode image of a carotid artery of a 30-year-old, healthy
male. White dashed line in the B-mode image shows the region shownin (b) and (c). (b) Assignment of the ﬁrst layer (between two points
x1 (1) and x1 (1)) in the previous phased-tracking method. LI and
MA are acronyms for the lumen-intima and media-adventitia interfaces, respectively. (c) Assignment of x1 (1) and x1 (1) in the proposed
method.

A. Principle for Simulating RF Echoes from Normal
Arterial Walls
An RF echo signal, rf(n; x), in the n-th frame at depth
x, which is reﬂected from the arterial wall of a healthy subject, can be modeled by the sum of echoes, rfLI (n; x) andrfMA (n; x), from the lumen-intima and media-adventitia
interfaces, respectively, located at depths dLI (n) and2056

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dMA (n). In such a situation, rf(n; x) is expressed using a sinusoidal wave at the center frequency f0 and the envelopeenv(x) as follows:
rf(n; x) = rfLI (n; x) + rfMA (n; x),
rfLI (n; x) = env(x − dLI (n))
4πf0 (x − dLI (n)),
c0rfMA (n; x) = env(x − dMA (n))
· sin

· sin

4πf0 (x − dMA (n)),
c0⎧⎨0.5 − 0.5 · cos 2π x
∆Xpenv(x) =
⎩
0

(23)

(24)

(25)

(0 ≥ x ≥ ∆Xp ),(∆Xp < x) , (26)where ∆Xp is the pulse duration. In this study, a Hann
window was used for the envelope of an ultrasonic pulse,
and the center frequency, pulse duration, frame rate, andsampling frequency of simulated echoes were 7.5 MHz, 3
wavelengths, 286 Hz, and 40 MHz, respectively.
Displacements of the posterior carotid artery wall of ahealthy, 30-year-old male [same as Fig. 4(a)], which were
measured by the phased-tracking method described in Section II-A, were used as displacements of the lumen-intima
and media-adventitia interfaces, ∆dLI (n) = dLI (n)−dLI (1)and ∆dMA (n) = dMA (n) − dMA (1).
As described in Section III, in the case of a healthy
subject, there are only two dominant echoes from thelumen-intima and media-adventitia interfaces, and only
the change in the entire intima-media thickness can be estimated by analyzing echoes from these interfaces. Therefore, the change in intima-media thickness, ∆hIMT (n) =∆dMA (n) − ∆dLI (n), was deﬁned as the true deformation.

Errors, eh , in changes in thickness, ∆h(n;x) and ∆h̄(n; x),estimated by the previous and proposed methods were obtained as follows:eh =|∆h(nmax ) − ∆hIMT (nmax )|× 100,|∆hIMT (nmax )|(27)

where ∆h(n) is ∆h(n;x) or ∆h̄(n; x), and tmax = nmax · T
is the time when ∆hIMT (n) is maximum.
B. Improvement of Deformation Estimates Using the
Proposed Method
Fig. 6(a) shows RF echo lines simulating those reﬂectedfrom the lumen-intima and media-adventitia interfaces
during one heart cycle. Fig. 6(b) shows the M-mode image obtained from the simulated RF echo lines shown in
Fig. 6(a). In this section, the initial intima-media thickness, dMA (1) − dLI (1), at the ﬁrst frame in (24) and (25)was set at 0.45 mm, which was obtained from Fig. 4. Byreferring to the M-mode image shown in Fig. 6(b), theinitial positions of the lumen-intima and media-adventitia
boundaries were assigned manually at the ﬁrst frame (timet = 0). With respect to multiple points between the assigned lumen-intima and media-adventitia boundaries, velocities, vm (n), at each frame were estimated as shown in
Fig. 6(c), and the instantaneous position of each point,
xm (n), was tracked using the phased-tracking method.
The estimated instantaneous positions of the lumen-intima
and media-adventitia boundaries are shown by white lines
in Fig. 6. Based on the instantaneous positions of thepoints assigned at t = 0 between the lumen-intima andmedia-adventitia boundaries, the rate of change in thickness at each depth, xm (n), was obtained by the previous
and proposed methods as shown in Figs. 6(d) and (e), respectively. In Fig. 6(e), the thickness of a layer, ML · ∆x,
was set to be the width at −20 dB of the maximum magnitude of the quadrature demodulated signal shown in Fig. 5.
The width at −20 dB was determined to be 0.48 µs, whichcorresponds to a distance of 370 µm at a sound speed of
1540 m/s. Along the instantaneous positions of each pointat respective frames, the rate of change in thickness was integrated with respect to time, and the change in thickness
at each depth, xm (n), was obtained by the previous andproposed methods as shown in Figs. 6(f) and (g). Fig. 6(h)shows the actual change in thickness.
As shown in Fig. 6(f), the magnitudes of changes inthickness near the luminal surface estimated by the previous method became smaller than the actual change inthickness as described in Section II. However, as shownin Fig. 6(g), compounded changes in thickness, ∆h̄(n; x),obtained by the proposed method were in good agreementwith the actual changes in thickness shown in Fig. 6(h).
Figs. 7(a) and 8(a) show the same actual change in thickness. Figs. 7(b) and 8(b) show waveforms of changes inthickness at points estimated by the previous and proposed methods, respectively, and Figs. 7(c) and 8(c) show
the distributions of changes in thickness at t = tmax overlaid on the echo magnitude in the ﬁrst frame (t = 0). Errors in the estimated changes in thickness obtained by the
proposed method were only 0.19 ± 0.04% (mean ± standard deviation) as compared with 21.2 ± 24.1% obtainedby the previous method.
As shown in Fig. 8(c), changes in thickness estimatedby the previous method around the lumen-intima interface
were reduced as described in Section III. Such an artiﬁcial
spatial variation of the changes in thickness estimated by
the previous method was suppressed as shown in Fig. 7(c),and the change in thickness estimated at each depth is ingood agreement with the change in intima-media thickness, which is deﬁned as the true deformation using the
proposed method.
C. Required Thickness of an Assigned Layer
In this section, errors in changes in thickness estimatedwith diﬀerent thicknesses, ML · ∆x, of an assigned layer
were investigated to determine the required layer thickness. As shown in Fig. 4, the typical thickness of theintima-media complex of a carotid artery of a healthy subject without intimal thickening is about 0.5 mm. There-hasegawa and kanai: modification of phased-tracking method and artery wall deformation

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Fig. 6. Results of simulation experiments. (a) Simulated RF echo. (b) Magnitude of demodulated signal. (c) Velocity, vm (n). (d) and(e) Rates, ∆hm (n), of change in thickness obtained by the previous and proposed methods, respectively. (f) and (g) Changes in thickness,∆hm (n), obtained by the previous and proposed methods, respectively. (h) Actual change in thickness.

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Fig. 7. Results of simulation experiments obtained by the previous
phased-tracking method. (a) Waveform of the actual change in thickness. (b) Waveforms of changes in thickness estimated at various
depths. (c) Magnitude of echo, actual change in thickness and estimated changes in thickness at tmax when the actual change in thickness is maximum.

fore, RF echoes were simulated for diﬀerent cases of
intima-media thicknesses of 0.4, 0.5, and 0.6 mm basedon the principle described in Section IV-A.
In Fig. 9, errors in changes in thickness estimated by the
proposed method are plotted as a function of the thickness,
ML · ∆x, of an assigned layer. As shown in Fig. 9, errors
were reduced by increasing the layer thickness, ML · ∆x.
However, a larger layer thickness worsens the spatial resolution in the estimation of the change in thickness. Thus,
it is desirable for the layer thickness, ML · ∆x, to be as
small as possible. As described in Section III, the duration of the ultrasonic pulse determines the lower limit of
the layer thickness, ML · ∆x, and this lower limit is foundto be the width at −20 dB of the maximum magnitudeof the quadrature demodulated signal. From these results,
the layer thickness, ML ·∆x, was determined to be 385 µm(ML = 20).

Fig. 8. Results of simulation experiments obtained by the proposed
method. (a) Waveform of the actual change in thickness. (b) Waveforms of changes in thickness estimated at various depths. (c) Magnitude of echo, actual change in thickness and estimated changes inthickness at tmax when the actual change in thickness is maximum.

V. In Vivo Experiments in a Human
Carotid Artery
Figs. 10(a) and (e) show the same electrocardiograms ofa 30-year-old, healthy male. Fig. 10(b) shows the RF echolines obtained in the region shown by the white, dashedline in Fig. 4(a). The frame rate and sampling frequencyof simulated echoes were 286 Hz and 40 MHz, respectively.

Fig. 9. Errors in changes in thickness estimated by the proposed
method. Errors are plotted as a function of the layer thickness, ML ·∆x, for diﬀerent cases of IMTs.

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Fig. 10. Results of in vivo experiments in a carotid artery of a 30-year-old, healthy male. (a) and (e) Electrocardiograms. (b) Measured
RF echo. (c) Magnitude of demodulated signal. (d) Velocity, vm (n). (f) and (g) Rates, ∆hm (n), of change in thickness obtained by theprevious and proposed methods, respectively. (h) and (i) Changes in thickness, ∆hm (n), estimated by the previous and proposed methods,
respectively.

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Fig. 11. Results of in vivo experiments obtained by the previous
phased-tracking method. (a) Waveforms of changes in thickness estimated at various depths. (b) Magnitude of echo and estimatedchanges in thickness at t = t0 .

Fig. 12. Results of in vivo experiments obtained by the proposed
method. (a) Waveforms of changes in thickness estimated at various
depths. (b) Magnitude of echo and estimated changes in thickness at
t = t0 .

Fig. 10(c) shows the M-mode image obtained from themeasured RF echo lines shown in Fig. 10(b). By referringto the M-mode image shown in Fig. 10(c), the initial positions of the lumen-intima and media-adventitia boundaries were assigned manually at the ﬁrst frame (time t = 0)
by inspecting the M-mode image. With respect to multiple points between the assigned lumen-intima and mediaadventitia boundaries, velocities, vm (n), at each point oftime were estimated as shown in Fig. 10(d), and the instantaneous position of each point was tracked using thephased-tracking method. The estimated instantaneous positions of the lumen-intima and media-adventitia boundaries are shown by white lines in Fig. 10. Based on the
instantaneous positions of the points assigned at t = 0 between the lumen-intima and media-adventitia boundaries,
the rate of change in thickness at each depth, xm (n), wasobtained by the previous and proposed methods as shownin Figs. 10(f) and (g), respectively. Along the instantaneous positions of each point at respective frames, the rateof change in thickness was integrated with respect to time,
and the change in thickness, ∆h(n; x), at each depth was
obtained by the previous and proposed methods as shownin Figs. 10(h) and (i), respectively.
Figs. 11(a) and 12(a) show waveforms of estimatedchanges in thickness at respective points, and Figs. 11(b)and 12(b) show the distributions of changes in thickness at
t = t0 overlaid on the echo magnitude at the ﬁrst frame. As
shown in Fig. 11(b), the magnitude of changes in thickness
near the luminal surface estimated by the previous method
became smaller, as did those of the simulation experiments
shown in Section IV. Changes in thickness between thelumen-intima and media-adventitia boundaries should beshown to be homogeneous because there are only two dominant echoes from these boundaries, and echoes from otherscatterers in the wall hardly contribute to estimation ofchanges in thickness. As shown in Fig. 12(b), changes inthickness estimated by the proposed method have an almost homogeneous distribution, as also was the case in thesimulation experiments.
As shown in Fig. 11(b), changes in thickness estimatedby the previous method around the lumen-intima interface
were reduced as described in Section III. As in the case of
the simulation experiments, such an artiﬁcial spatial variation of the changes in thickness estimated by the previous method was suppressed using the proposed method
as shown in Fig. 12(b). From these results, the proposed
method was proved to properly show the deformation of
the arterial wall, at least in the case in which there are
two dominant echoes from the lumen-intima and mediaadventitia interfaces.

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Fig. 13. B-mode images of femoral arteries excised from two patientswith arteriosclerosis obliterans. (a) 78-year-old male. (b) 72-year-old
male.

VI. In Vitro Experiments Using Excised
Diseased Arteries

Figs. 13(a) and (b) show B-mode images of femoral arteries excised from two patients, 78-year-old and 72-yearold males, with arteriosclerosis obliterans, respectively. After surgical extraction, arteries were immediately kept incold storage and were measured within 5 days. These twoarteries were placed in a water tank ﬁlled with 0.9% saline
solution at the room temperature, and the change in internal pressure was applied by a ﬂow pump. During the application of the change in internal pressure, RF lines wereacquired along the ultrasonic beams as shown by white vertical arrows in Figs. 13(a) and (b). Then, as in the in vivo
experiments, changes in thickness of the arterial walls were
estimated by the previous and proposed methods as shownin Figs. 14–17. Figs. 14(a), 15(a), 16(a), and 17(a) show
waveforms of internal pressure measured with a catheter(model 110-4, Camino Co., Ltd., San Diego, CA) locatedat the edge of the distal side of the artery. Figs. 14(b) and16(b) show waveforms of changes in thickness of the 78year-old and 72-year-old males, respectively, obtained by
the previous method, and Figs. 15(b) and 17(b) show thoseobtained by the proposed method. Figs. 14(c), 15(c), 16(c),and 17(c) show the magnitudes of quadrature demodulated signals at time t = 0 and the changes in thickness
at time t = tmax when the internal pressure was maximum. As in cases of the simulation and in vivo experiments, magnitudes of changes in thickness near the lumenintima interfaces estimated by the previous method were
small in comparison with those estimated by the proposed
method. Such decreases in magnitudes of changes in thickness shown in Figs. 14(c) and 16(c) are considered to be
artifacts as described in Section III, and such artifacts werereduced by the proposed method as shown in Figs. 15(c)and 17(c).

Fig. 14. Results of in vitro experiments obtained by the previous
phased-tracking method (78-year-old male). (a) Internal pressure.
(b) Waveforms of changes in thickness estimated at various depths.
(c) Magnitude of echo and estimated changes in thickness at t =tmax .

VII. Discussion
In cases of diseased arteries shown in Fig. 13, there
are spatial variations in estimated changes in thickness
within arterial walls in comparison with an artery of ahealthy subject. As shown in Figs. 15(c) and 17(c), thenumber of inﬂection points of spatial distribution of estimated changes in thickness were reduced in comparison
with those of the previous method shown in Figs. 14(c)and 16(c) due to the deterioration of the spatial resolution
caused by the enlargement of the thickness of an assigned
layer. However, as described in Section IV-C, a layer thickness of at least the width at −20 dB of the maximum magnitude of the quadrature demodulated signal is required for
reducing the artifact described in Section III. The elastic
property of a diseased artery is heterogeneous, and the spatial variation in estimated changes in thickness within thearterial wall shown in Figs. 15(c) and 17(c) will be causedby such a heterogeneous distribution of elasticity. However,
the eﬀects of attenuation, diﬀraction, interference between
echoes, and noise—which also inﬂuence the estimation ofchanges in thickness—were not considered in this study.
The spatial variation in changes in thickness caused by aheterogeneous distribution of elasticity cannot be diﬀerentiated from that due to such eﬀects. Therefore, further
studies using phantoms with known mechanical properties
such as those used in [11] are necessary for the validation

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Fig. 15. Results of in vitro experiments obtained by the proposed
method (78-year-old male). (a) Internal pressure. (b) Waveforms ofchanges in thickness estimated at various depths. (c) Magnitude ofecho and estimated changes in thickness at t = tmax .

Fig. 17. Results of in vitro experiments obtained by the proposed
method (72-year-old male). (a) Internal pressure. (b) Waveforms ofchanges in thickness estimated at various depths. (c) Magnitude ofecho and estimated changes in thickness at t = tmax .

of the estimated changes in thickness within the wall likethose shown in Figs. 15(c) and 17(c).
In addition, in this study, correlation estimators insteadof rates of changes in thickness were compounded because
the rate of the change in thickness contains no information on the signal-to-noise ratio of the echo signal used for
estimating the change in thickness. By compounding thecorrelation estimators in (17), the contribution of a correlation estimator, which was obtained from the hypoechoic
region (low signal-to-noise ratio), is suppressed. However,
the eﬀects of such compounding were not suﬃciently investigated in this study, as it concentrated on the reduction ofan artifact using the proposed method in cases of healthy
subjects as described in Section III. Further investigationsof the eﬀects of compounding also are necessary.
In this study, measurements of changes in thickness
were conducted for the posterior walls. As shown in
Fig. 4(a), echoes from the lumen-intima interface of theanterior wall are often faint in comparison with those fromthe posterior wall. Such a phenomenon may be due to inﬂuences of echoes due to sidelobes of an ultrasonic beam,
which are scattered by the soft tissue between the skinsurface and the anterior wall.
Fig. 16. Results of in vitro experiments obtained by the previous
phased-tracking method (72-year-old male). (a) Internal pressure.
(b) Waveforms of changes in thickness estimated at various depths.
(c) Magnitude of echo and estimated changes in thickness at t =tmax .

VIII. Conclusions
In the present study, our previous method for measuring the change in thickness of the arterial wall caused byhasegawa and kanai: modification of phased-tracking method and artery wall deformation

the heartbeat was modiﬁed to reduce an artifact in a deformation image of the arterial wall.
In the case of a carotid artery of a healthy subject,
there are only two dominant echoes from the lumen-intima
and media-adventitia interfaces. In such a situation, only
the change in the entire intima-media thickness can be estimated using ultrasound. However, changes in thickness
estimated by the previous phased-tracking method show
the artiﬁcial spatial variation. In this study, the phasedtracking method was modiﬁed to reduce this artifact. In
simulation experiments, it was found that such artiﬁcial
spatial variation was reduced by the proposed method, andchanges in thickness estimated by the proposed method
corresponded to that in the entire intima-media thickness. In addition, in in vivo experiments, a similar distribution of changes in thickness was obtained. A simple
model corresponding to the measurement in carotid arteries of healthy subjects, in which there are only two dominant echoes from the lumen-intima and media-adventitia
interfaces, was used in this study to elucidate the eﬀect
of modiﬁcation. Therefore, more complex cases, in which
there are more dominant echoes from the arterial wall, as
in cases of atherosclerotic plaque, should be investigatedin the future.

Acknowledgment
This work was supported by the Ministry of Education,
Science, Sports and Culture, and is partially supportedby the Mazda Foundation, the Nakatani Electronic Measuring Technology Association of Japan, and the Inamori
Foundation.

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Hideyuki Hasegawa was born in Oyama,
Japan, in 1973. He received the B.E. degreefrom Tohoku University, Sendai, Japan, in
1996. He received the Ph.D. degree from Tohoku University in 2001. He is presently a lecturer in the Graduate School of Engineering,Tohoku University.
His main research interest is medical ultrasound, especially diagnosis of atherosclerosis
based on measurement of mechanical properties of the arterial wall.
Dr. Hasegawa is a member of the IEEE,
the Acoustical Society of Japan, the Japan Society of Ultrasonics in
Medicine, and the Institute of Electronics, Information and Communication Engineers.

Hiroshi Kanai (M’98) was born in Matsumoto, Japan, on November 29, 1958. Hereceived a B.E. degree from Tohoku University, Sendai, Japan in 1981, and M.E. and the
Ph.D. degrees, also from Tohoku University,
in 1983 and in 1986, both in electrical engineering.
From 1986 to 1988 he was with the Education Center for Information Processing, Tohoku University, as a research associate. From1990 to 1992 he was a lecturer in the Department of Electrical Engineering, Faculty of Engineering, Tohoku University. From 1992 to 2001 he was an associate
professor in the Department of Electrical Engineering, Faculty of Engineering, Tohoku University. Since 2001 he has been a professor in
the Department of Electronic Engineering, the Graduate School ofEngineering, Tohoku University.
His present interests are in ultrasonic measurement and digital
signal processing for diagnosis of heart diseases and arteriosclerosis.
Dr. Kanai is a member of the Acoustical Society of Japan, theInstitute of Electronics Information and Communication Engineering of Japan, the Japan Society of Ultrasonics in Medicine, Japan
Society of Medical Electronics and Biological Engineering, and theJapanese Circulation Society.