REGULAR PAPER

Japanese Journal of Applied Physics 53, 07KF21 (2014)
http://dx.doi.org/10.7567/JJAP.53.07KF21

Improvement of myocardial displacement estimation using subkernels
for cross correlation between ultrasonic RF echoes
Dai Asari1, Hideyuki Hasegawa2,1, and Hiroshi Kanai1,2*
1Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan
E-mail: kanai@ecei.tohoku.ac.jp
2

Received November 29, 2013; accepted March 30, 2014; published online June 24, 2014
Speckle tracking is a useful diagnostic method for assessing the cardiac function from ultrasonic echoes. Some factors inﬂuence the performanceof the conventional speckle tracking method. Deformation due to myocardial contraction and relaxation decreases the correlation between RF
echoes. Also, if a strong echo, such as echoes from the epicardium, is included in a correlation kernel, the displacement estimated from the kernel
becomes close to the displacement of the epicardium even when the myocardium in the middle of the heart wall is the target to be tracked. To
overcome such a problem, in the present study, we proposed a two-step tracking method. In the ﬁrst step, the displacement is coarsely estimatedusing a correlation kernel of size similar to that in conventional speckle tracking of (13.8°, 9.1 mm) in the lateral and axial directions. The kernel isdivided into small subkernels (2.8°, 1.9 mm). By estimating the correlation coefﬁcient with respect to each subkernel and averaging correlation
coefﬁcients obtained from all subkernels, the contribution of a peculiar strong echo included in one of the subkernels can be suppressed. In thesecond step, the residual displacement is ﬁnely estimated using a smaller kernel (13.8°, 3.6 mm). Using a smaller kernel, the inﬂuence of
myocardial deformation can be suppressed, but there might be multiple regions that have echo patterns similar to that in the kernel, leading to
tracking errors. Therefore, the search region in the second step is narrowed because the coarse displacement has already been estimated andcompensated in the ﬁrst step. In the present study, the proposed method was validated using a phantom made of urethane rubber, which was
deformed by an actuator. The displacement of the phantom could be estimated with a lower error of 0.059 mm by the proposed method comparedto the error in the conventional method of 0.097 mm. Furthermore, the proposed method was applied to in vivo measurement of the human heart.
The myocardial displacement could be estimated successfully even when the epicardium was included in a correlation kernel. These results showthat the proposed method provides a more accurate and robust estimation of the myocardial displacement.
© 2014 The Japan Society of Applied Physics

1.

Introduction

Circulatory diseases are increasing due to the westernizationof diet, lack of exercise, and aging of society. Therefore, early
detection of such diseases is very important. Ultrasonicdiagnosis is noninvasive to the human body and costeffective. Therefore, diagnostic ultrasound is widely used
for diagnosis of the circulatory system, such as arteries1–10)
and the heart.11–16) Although the morphological information
obtained using ultrasonic diagnostic equipment is useful,functional imaging of tissues would provide beneﬁcial
diagnostic information.17–23) Particularly in echocardiography, myocardial strain and strain rate have also been shown
to be effective in the diagnosis of myocardial function.22,24–27)
For the assessment of myocardial motion and deformation,
the speckle tracking method,28–31) which estimates motion
using backscattered ultrasonic echoes by regional patternmatching techniques,32) is widely used.
However, in a conventional speckle tracking algorithm,
myocardial deformation caused by contraction and relaxation
often degrades the accuracy of displacement estimation.33,34)
In the calculation of the cross-correlation function between
ultrasonic RF echoes, motion accompanied by the deformation of cardiac muscle (not only parallel motion) decreases
the correlation between RF signals and leads to an estimation
error. Also, if a strong echo, such as an echo from theepicardium, is included in a correlation kernel, the displacement estimated from the kernel becomes close to thedisplacement of the epicardium even when the displacementof the myocardium in the middle of the heart wall, which islocated at the center of the kernel, is desired to be estimated.
To overcome the above problems, in the present study, we
employed a two-step tracking method.35–38) In the ﬁrst step,
the motion of a target point is coarsely estimated. During thisprocess, in the present study, the kernel was divided into
small subkernels to suppress the inﬂuence of a peculiar strong
echo. Then, the residual small displacement was ﬁnely
estimated in the second step using a smaller correlation
kernel to reduce the inﬂuence of the myocardial deformation.
The novelty of this method is application of the divided
kernel to suppress the inﬂuence of strong echo. In the present
study, the proposed approach was validated by a basic
experiment using a silicone phantom deformed by anactuator. Also, we conducted an in vivo measurement of ahuman heart to show the feasibility of the proposed method.
2.

Principles

2.1

First step: Coarse estimation with divided kernel
In the present study, myocardial two-dimensional (2D)
displacement was estimated by speckle tracking using thenormalized cross-correlation function between ultrasonicRF echoes. In the ﬁrst step, a larger kernel in the lateraland axial directions, whose central position was p1, was used
for coarse displacement estimation. Typically, a larger kernel
is desirable to increase the uniqueness of speckle patterns,
thus a larger kernel in general realizes a more robust
displacement estimation at the expense of the spatial
resolution.33,39,40) In this step, to suppress the inﬂuence of apeculiar strong echo, the larger kernel is divided into 5 © 5blocks (subkernels).
With respect to the lag p ¼ ð; zÞ between kernels in
two frames, the normalized correlation function ij ð; zÞ(i ¼ 2; 1; . . . ; 2; j ¼ 2; 1; . . . ; 2) was obtained foreach subkernel. By averaging correlation functions
fij ð; zÞg of all subkernels, contributions of subkernels
are equalized even when a subkernel contains a peculiar
strong echo. The total correlation function ð; zÞ is deﬁned
by

07KF21-1© 2014 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 53, 07KF21 (2014)

D. Asari et al.

(a)

(a)
searchregionilaser displacement meter
ultrasonic probe
plate

(b)
10 mm

couplerd0jp0kernell2

p1

siliconephantom
fixed based4
l0

actuator(b)
Fig. 2. (Color online) (a) Schematic of experiment using silicone
phantom. (b) Points of interest for displacement estimation overlaid on
B-mode image of phantom.

p0
kernelsearchregionp1 p2

Fig. 1. (Color online) Illustration of displacement estimation by the
proposed method. (a) First step using divided subkernels. (b) Second stepusing a smaller kernel.
2 X
2Xð; zÞ ¼

3.

Basic experiment

3.1

wij ij ð; zÞi¼2 j¼2
2 X
2
X

;

ð1Þ

wij

i¼2 j¼2

wij ¼

tracking with a smaller kernel in the lateral and axial
directions. The size of the search region (0.375°, 0.05 mm)corresponded to the lateral and axial intervals of the sampled
RF signals because displacement larger than the samplinginterval was compensated in the ﬁrst step.



1
1 2
2
exp

ði
þ
j
Þ
;
2 2
2 2

ð2Þ

where · (= 0.8) is the standard deviation of a 2D Gaussian
window wij. By equalizing contributions of subkernels andusing the weight wij, which is maximum at the center of theoriginal kernel, the inﬂuences of the peculiar strong echo canbe suppressed and the displacement of the point of interest(center of the original kernel) can be estimated.
In Fig. 1(a), relative positions of kernels p1 and p2 in two
consecutive frames are illustrated at a certain lag p ¼
ð; zÞ. The position of the kernel in the post frame is deﬁned
as p2 = p1 + ¤p. The size of the search region (range of lag)was set at (0.750°, 0.51 mm) in the lateral and axial directionsin the ﬁrst step, which was larger than the displacement of theheart wall in two frames of 0.125 mm (corresponding to the
maximum myocardial velocity of 90 mm/s at a frame rate of
720 Hz41)). The coarse displacement ðu ; uz Þ was determinedfrom the lag ðb; bz Þ, which maximizes the total correlation
function ð; zÞ.
2.2 Second step: Fine displacement estimation using
smaller kernel

In the second step, a smaller kernel is used to estimate theﬁne displacement of the point of interest because a smaller
kernel is less affected by myocardial deformation. However,there might be multiple regions having echo patterns similar
to that in a smaller kernel.42,43) Therefore, as shown in
Fig. 1(b), a search region (0.375°, 0.05 mm) in the lateral andaxial directions, which is smaller than that used in the ﬁrst
step, is assigned around the position p1, and the residual
displacement is ﬁnely estimated by conventional speckle

Basic experimental setup
The proposed two-step tracking method was validated by abasic experiment using a phantom (60 © 80 © 80 mm3) madeof urethane rubber. The phantom contains 1% carbon powder
by weight to induce sufﬁcient scattering from the insideof the phantom. As shown in Fig. 2(a), the phantom was
attached to a ﬁxed base and the phantom was deformed by anactuator. The frequency of sinusoidal motion of the actuator
was set at 8 Hz. The displacement of points of interest ðli ; dj Þ(i ¼ 0; 1; 2; j ¼ 0; 1; . . . ; 4) inside the phantom shown in
Fig. 2(b) were estimated by the proposed method and theconventional method, and the accuracy of each method wasevaluated. The displacement of the plate attached to theactuator was measured using a laser displacement meter(Keyence LK-G155) to obtain the spatial distribution of true
displacements in the phantom.
The spatial distribution of true displacements was obtainedby the ﬁnite-element method (FEM)44) using the displacement of the plate measured using laser. The FEM analysis
was performed with a commercial software (Hokuto
FEMLEEG version 4.2). By FEM analysis, the amplitudeof displacement A(l) at each horizontal position l in thephantom can be estimated as shown in Fig. 3(b). In thepresent study, the magnitude of displacement applied to anedge (l = 60 mm) of the phantom (corresponding to thevibrating plate) was set at 1 mm in the FEM analysis. Using
amplitude A(l) estimated by the FEM, the true displacementx0 ðl; nÞ at the horizontal position l in the n-th frame isobtained as follows:x0 ðl; nÞ ¼ xlaser ðnÞ AðlÞ;Aðl ¼ 60 mmÞ

ð3Þ

where xlaser(n) is the displacement of the vibrating platemeasured using laser.
For evaluation of the accuracy, the root mean square error(RMSE) ¾ was calculated using the true displacement x0 ðl; nÞand the estimated displacement xðl; d; nÞ at horizontal andvertical positions l and d as follows:

07KF21-2© 2014 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 53, 07KF21 (2014)

siliconphantom

−0.4
−0.6

Δd

−0.8

0

10

20

30

40

50

Δl

Wd

Wl
kernelbeam profile

60

position l [mm]1.0

Fig. 4. (Color online) Schematic of correlation kernel.

0.5
0.0

(a)

−0.5
−1.0
0.0

0.2

0.4

0.6

0.8

amplitude

displacement x laesr (s ) [mm]30 60 l [mm]

axial

−0.2

−1.0
0

(c)

lateral(b) 0.0

laser
displacement meter

displacement
distribution A ( l,d ) [mm](a)D. Asari et al.

1.0

time t [s]Fig. 3. (Color online) (a) Illustration of laser measurement of plate
vibrated by actuator. (b) Distribution of amplitude of displacements estimatedby ﬁnite-element method. (c) Displacement of plate attached to actuatormeasured by laser displacement meter.

15000
10000
5000
0
−5000
−10000PW epicardium

IVS

0

20

40

60

80

100

120

position [mm]

(b)

(c)
10 mm

vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
u
4 X
4 X
N 1
u 1 X
¼t
fx0 ðli ; nÞ  xðli ; dj ; nÞg;M  N j¼0 i¼0 n¼0

IVS

ð4Þ
PW

where N and M (= 25) are the numbers of frames andmeasurement points used in the calculation of RMSE, andðli ; dj Þ are horizontal and vertical positions of each measurement point.
Ultrasonic RF echoes were acquired using a modiﬁed
ultrasound system (Hitachi-Aloka ¡-10) with a 3.75 MHz
phased array probe. Through the use of parallel receive
beamforming (PBF) with plane wave transmissions,45,46) the
frame rate of 720 Hz was realized. The maximum motion
velocity of the plate attached to the actuator was about
10 mm/s, which was much smaller than a typical motion
velocity of the heart wall of 50 mm/s.47–49) Therefore, theinterval in the calculation of the cross-correlation function
was set at 5 frames so that the displacement between twoframes became similar to that of the heart wall.41,42) The
lateral and axial spacing of the acquired RF data were 0.375°
and 51.3 µm (corresponding to a sampling frequency of
15 MHz), respectively. The myocardial displacement between
two consecutive frames is approximately 70 µm under atypical myocardial velocity of 50 mm/s and frame rate of
720 Hz. To accurately estimate such a small displacement, thecross-correlation function was interpolated by a factor of
ð120; 50Þ in the lateral and axial directions by reconstructive
interpolation50) to improve the resolution in the estimationof the displacement. The spacing of the cross-correlation
function after interpolation was [3.1 © 10¹3 deg (0.2 µm at
depth 40 mm), 1.0 µm] in the lateral and axial directions.
As shown in Fig. 4, the size of a correlation kernel in thelateral and axial directions ðWl ; Wd Þ were deﬁned on thebasis of the size of the point spread function (PSF) ofðlateral; axialÞ ¼ ðl; dÞ.41) The size of the correlation
kernel (Wl © Wd ) was deﬁned as

10 mmkernelcentral beam
epicardium

targetpoint
boundary

Fig. 5. (Color online) (a) RF signal and (b) B-mode image of human heart
which contains strong reﬂector, i.e., epicardium. (c) Correlation kernel andboundary indicated on B-mode image of phantom.

ðWl  Wd Þ ¼ 2ðl  l  d  dÞ;

ð5Þ

where ¡l and ¡d are the variable coefﬁcients. In the ﬁrst stepof the proposed method, ðl ; d Þ were set at ð1:0; 1:0Þ byreferring to our previous study.41) In the second step, toexamine the appropriate size of a correlation kernel, RMSEs
were evaluated at various values of ¡d from 0.1 to 0.8. The
lateral width of a correlation kernel ¡l was set at 1.0 because
the lateral size of the PSF is larger than the axial size andthere was no oscillation, such as that owing to the ultrasonicfrequency in the axial direction, in the lateral direction. The
size of the PSF ðl; dÞ was ð2:40; 2:28Þ mm. In theconventional speckle tracking method, the correlation kernel
size was the same as that of the proposed method in the ﬁrst
step.
Furthermore, in the actual in vivo measurement of theheart, amplitudes of echoes from strong scatterers, such as the
epicardium, are much higher than those from the myocardium, as shown in Figs. 5(a) and 5(b). To simulate theexistence of such strong echoes, a custom-made phantom(containing 1% graphite powder by weight), shown in
Fig. 5(c), was used. The phantom had a boundary, and theboundary generates stronger echoes than those from inside
the phantom.

07KF21-3© 2014 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 53, 07KF21 (2014)

D. Asari et al.

correlation
coefficient

(a)

0.08
0.07

(b)

1.0

(4)

0.8

(3)

(1)

0.6
(1)
(2)
(3)

0.4
0.2

(4)
(5)

(5)

(2)

(c) 1.000

0.06
0.1

0.2
0.3
0.4
0.5
0.6
0.7
α d (parameter of correlation kernel size)

correlation
coefficient

RMS error ε [mm/s]

0.09

0.8

Fig. 6. (Color online) RMSE  obtained for each parameter of thecorrelation kernel size in axial direction ¡d.

0.996
0.992
proposed method
conventional method

0.988
0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

time [s]displacement [mm]0.6
Fig. 8. (Color online) (a) Correlation coefﬁcients obtained fromsubkernels at maximum of total correlation function. (b) Assigned correlation
kernel and subkernels overlaid on B-mode image of phantom. (c) Maximum
correlation coefﬁcients obtained by the conventional and second step of the
proposed method.

0.4
0.2
0.0
−0.2
−0.4
−0.6
0.00

0.02

0.04

0.06
0.08
time [s]

0.10

0.12

0.14

Fig. 7. (Color online) True displacement (red) and estimateddisplacements (blue: conventional, green: proposed) at point ðl1 ; d2 Þ whenusing proposed method and conventional method.

3.2

Experimental results
Figure 6 shows RMSEs obtained at different f¡dg by the
proposed method. RMSE was minimum when ¡d was 0.4.
Therefore, the displacement estimated by the proposed
method at ¡d = 0.4 [correlation kernel size was (13.8°,
3.6 mm)] was compared with the displacement estimatedby the conventional method. Figure 7 shows examples ofdisplacement waveforms at point ðl1 ; d2 Þ obtained by the
FEM analysis, proposed method, and conventional speckle
tracking method. In the conventional speckle tracking
method, the correlation function was interpolated by a factorof ð120; 50Þ, which was the same as that in the second stepof the proposed method. As shown in Fig. 7, the displacement estimated by the proposed method is much closer to thetrue displacement, compared with that estimated by theconventional method. By estimating displacements at eachof 15 measurement points, RMSE ¾ values obtained by
the proposed and conventional methods were 0.059 and0.097 mm, respectively. It was conﬁrmed that RMSE was
reduced by 39.2% when using the proposed two-step tracking
method. However, the standard variations of RMSE obtainedby the proposed and conventional methods were 0.025 and
0.010 mm, respectively. The displacement estimation by the
proposed method was more accurate but less stable. In thisexperiment, amplitudes of the boundary at the edge of thekernels were high, and the displacement estimated from thekernel became similar to the displacement around the edge ofthe kernel, which was different from the displacement at thecenter of the kernel (= point of interest).
Figure 8(a) shows correlation coefﬁcients fij ð; zÞg
obtained from the respective subkernels when the total

correlation function £(¤p) is maximum. By equalizing thecontribution of subkernels and applying the highest weight tothe central subkernel, the correlation coefﬁcient in the central
subkernel became the highest when the total correlation
function was maximum, as shown in Fig. 8(a). Also, thecorrelation coefﬁcient in the second step was, in total, higher
than that obtained by the conventional method because asmaller kernel was less inﬂuenced by the myocardial
deformation and obtained a better match between echopatterns in two frames.
It is difﬁcult to estimate the displacement of a point ofinterest (the central point of the entire kernel in the ﬁrst step)when the subkernel is large and a strong scatterer, which isdistant from the point of interest, is included in the central
subkernel, because the maximum distance between the strong
scatterer and the point of interest depends on the size of thesubkernel. A larger distance between a point of interest and astrong scatterer would leads to a larger error in the estimationof the displacement of the point of interest because theestimated displacement is signiﬁcantly inﬂuenced by thestrong scatterer and the displacement of the strong scatterer isdifferent from the displacement of a scatterer at the point ofinterest. Therefore, smaller subkernels are desirable. However, the uniqueness of the echo pattern in a subkernel isdegraded and the accuracy in the displacement estimation
would be degraded when subkernels are too small. In thepresent study, RMSEs of the estimated displacements were
evaluated for various numbers of divisions of the kernel inthe ﬁrst step. As shown in Fig. 9, RMSE tends to increase
on increasing the number of divisions. In the present study,
ﬁve divisions were employed because RMSE increases
signiﬁcantly between 5 and 6 divisions.
Furthermore, to examine the appropriate weight functionwij, RMSEs of the estimated displacements were also
evaluated under the various values of the standard deviation· of the Gaussian distribution. In Fig. 10, RMSE almost
converges to 0.055 mm at · = 0.8. A smaller · corresponded
to a smaller effective size of a kernel, and RMSE was larger
when using a smaller kernel. However, a kernel is desired to
be as small as possible for a better spatial resolution in the07KF21-4© 2014 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 53, 07KF21 (2014)

D. Asari et al.

variance of displacement [mm]

0.20
0.16

(b)

(a)

n=3
n=4
n=5
n=6
n=7

10 mm

ultrasonic probe

RV

apex
RV

0.12

IVS

0.08

LV

basal

LV

kernel target
point

Ao

PW

LA

0.04
0.00
0.0

0.1

0.2

0.3

0.4

Fig. 11. (Color online) (a) Illustration of acquisition area of RF echo
signals in long-axis view of left ventricle. (b) Velocity is estimated at theyellow point displayed on B-mode image.

0.5

time [s]Fig. 9. (Color online) Variance of estimated displacement in lateral
direction at point ðl2 ; d2 Þ.

(a)

ECG

R−wave
first

PCG

(b)

(b)

0.06

0.5

0.6

0.7

0.8
0.9
variance σ

1.0

1.1

1.2

σ = 0.5
σ = 0.6
σ = 0.7
σ = 0.8
σ = 0.9σ = 1.0
σ = 1.1
σ = 1.2

0.2

40
20
0
−20
−40
−60
−80

0.98
0.96
0.94
0.92
0.90
0.88
0.86
0.00

−1

0
position i

1

2

Fig. 10. (Color online) (a) RMSE obtained by each variance ·. (b) Weightfunction wij ( j = 0).

displacement estimation. Therefore, in the present study,· = 0.8 was used.
4.

0.05

0.10

0.15

0.20

0.25

time [s]

0.1

0.0
−2

proposed method
conventional method

−100
−120
1.00

(c)

0.4

0.3
amplitude

velocity inlateral direction

0.07

0.05

60

correlation coefficient

RMS error ε [mm](a) 0.08

In vivo measurement of human heart

Figure 11(b) shows a B-mode image of the heart obtained
from a healthy 22-year-old male. The ultrasonic data wereacquired in the long-axis view of the left ventricle, as
illustrated in Fig. 11(a). The ultrasonic data were composedof 144 scan lines at lateral intervals of 0.375°, and the frame
rate was 560 Hz. The kernel size used for the ﬁrst and second
steps were (13.5°, 13.2 mm) and (6.8°, 6.6 mm), respectively.
As in the basic experiment, the correlation kernel size
was determined by PSF ðl; dÞ ¼ ð3:68; 2:35Þ mm andðl ; d Þ ¼ ð1:0; 0:4Þ. The sizes of search regions were thesame as those used in the basic experiment. The instantaneous motion velocity at a point assigned in the posteriorwall (PW) of the left ventricle was estimated by the proposedand conventional methods.

Fig. 12. (Color online) In vivo experimental results.
(a) Electrocardiogram and phonocardiogram. (b) Estimated velocities.
(c) Maximum correlation coefﬁcients.

Figure 12(a) shows the electrocardiogram (ECG) andphonocardiogram (PCG). Figures 12(b) and 12(c) show theestimated velocities in the lateral direction of the PW aroundthe R-wave and the estimated maximum correlation coefﬁcients. The red and blue lines indicate the results obtainedby the proposed and conventional methods, respectively. In
the period from 0.07 to 0.10 s, the correlation coefﬁcient
is signiﬁcantly decreased, presumably by the myocardial
deformation. During that period, a more deviant velocity
was found in the velocity waveform estimated by the conventional method. With the proposed method, the correlation
coefﬁcient was signiﬁcantly increased, and the deviation in
the estimated velocity was suppressed.
Figure 13 shows RF signals obtained along two scan lines
in the correlation kernels. The time shifts between RF signals
shown in Figs. 13(1) and 13(2) were compensated by the
proposed and conventional methods. Figures 13(a) and 13(b)show RF signals in the scan lines at the center and edge of thekernel. RF signals in the 46th and 47th frames (signiﬁcantdecrease in the correlation coefﬁcient was observed in these07KF21-5© 2014 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 53, 07KF21 (2014)
(a−2)

300

300

150

150

amplitude

amplitude(a−1)

D. Asari et al.

0

−150
−300

0

2

4

6

8

10

12

−300

(a−2)
100th frame
10 mm

10 mm

0

0.18 s−150

46th frame
47th frame(a−1)
first frame

46th frame
47th frame
0

2

4

6

8

10

apex
side

12

kernel

0

−100

150
0

−150

−300
4.0

4.5

5.0

5.5

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4.0

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(b−1)

500

500

amplitude

1000

amplitude

5.5

6.0

(b−2)

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0

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0

2

4

6

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amplitude

1000

500
0

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−1000
1.0

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distance [mm]

2.5

(b−2)
100th frame

0

2

4

6

kernel
10

8

basal
side

10 mm

apex
side

basal
side

12

Fig. 14. (Color online) Position of interest and correlation kernel obtainedby (a) proposed method and (b) conventional method. (1) First frame inanalysis period. (2) 100th frame.

0

−1000
1.0

0.18 sapex
side

46th frame
47th frame

−500

1.5

(b−1)
first frame
10 mm

−500

46th frame
47th frame

1000

amplitude

5.0

distance [mm]distance [mm]

−1000

basal
side

300

100

amplitude

amplitude

300

apex
side

basal
side

1.5

2.0

2.5

distance [mm]Fig. 13. (Color online) RF signals in scan lines at the center (a) andedge (b) of kernel. RF signals were analyzed by proposed method (1) andconventional method (2).

frames) are presented. In this case, the amplitudes of echoes
in the scan line at the edge [Fig. 13(b)] are signiﬁcantly
higher than those in the central scan line. Therefore, in theconventional method, RF signals in the scan line at the edge
match better than those in the central scan line and, thus, thedisplacement of the point of interest (center of the kernel)
cannot be estimated correctly. On the other hand, in the
proposed method, RF signals in the central scan line match
better than those in the scan line at the edge, and thedisplacement at the point of interest can be estimated.
Furthermore, the improvement in displacement estimation
was also evaluated by visual inspection of the motion of thepoint of interest. In Fig. 14, the positions of the point ofinterest in the ﬁrst and 100th frames are shown on thecorresponding B-mode images. The sector drawn in red
indicates the correlation kernel, and its movement represents
the estimated displacement of the heart wall between 100
frames. The ﬁrst frame corresponds to 0 s, and the 100thframe is at approximately 0.18 s in Fig. 12. In the result
obtained by the conventional method, shown in Fig. 14(b),there is an erroneous movement of the point of interest
toward the base of the heart, although the corresponding
movement was not seen by visual inspection because strong
echoes in the base side, which moved to the base side, were
included in the correlation kernel. In the results obtained by
the proposed method [Fig. 14(a)], such erroneous movement
did not arise owing to the suppression of the contributions ofsuch strong echoes.

5.

Conclusions

In the present study, we proposed a two-step tracking method
to estimate the displacement of a deforming object, such as
the heart wall. We conducted an experiment using a silicone
phantom to evaluate the accuracy of our proposed method.
The RMSE obtained by the proposed method was smaller
than that obtained by the conventional method. Furthermore,
the proposed method was applied to in vivo measurement of
the human heart, and the erroneous velocity estimation was
suppressed when using the proposed method. These results
show the potential of the proposed method for more accurate
measurement of the cardiac function.

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