Reprinted from

REGULAR PAPER

Evaluation of Rate of Change in Thickness of Heart Wall by Measuring Time Variationof Ultrasonic Integrated Backscatter during a Cardiac Cycle
Hiro Shida, Hideyuki Hasegawa, and Hiroshi Kanai

Jpn. J. Appl. Phys. 51 (2012) 07GF05# 2012 The Japan Society of Applied Physics

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REGULAR PAPER

Japanese Journal of Applied Physics 51 (2012) 07GF05
DOI: 10.1143/JJAP.51.07GF05

Evaluation of Rate of Change in Thickness of Heart Wall by Measuring Time Variationof Ultrasonic Integrated Backscatter during a Cardiac Cycle
Hiro Shida1 , Hideyuki Hasegawa1;2 , and Hiroshi Kanai1;2 
12Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan

Received November 18, 2011; accepted February 27, 2012; published online July 20, 2012
Integrated backscatter (IB) from the heart wall is gaining attention as a quantitative tissue characterization method and the cyclic variation (CV) in
IB during a cardiac cycle offers potential for the evaluation of myocardial contractility. Since there is large motion in the heart wall owing to theheartbeat, in the conventional method, the position of the region of interest (ROI) for calculating the IB is manually assigned in each frame during
one cardiac cycle. Moreover, the change in the size of the ROI during contraction and relaxation of the myocardium is not considered. In thisstudy, the phased tracking method was applied to multiple points in the heart wall for automatic tracking of the position and size of the ROI and,then, IB in the same site of the heart wall was measured in each frame by improving temporal resolution and spatial resolution in the axial
direction. As a result, cyclic variations, which differed site by site, were found. Furthermore, the rate of change in thickness was estimated by using
the interference cycle obtained by applying the discrete Fourier transform (DFT) to IB signals. According to the results, the rate of change inthickness estimated using the interference cycle of IB was in good agreement with that estimated by the phased tracking method. These results
indicate the possibility of estimating the rate of change in thickness using the IB signal. # 2012 The Japan Society of Applied Physics

1. Introduction

For the diagnosis of heart disease such as myocardial
infarction, hypertrophic cardiomyopathy, and dilated cardiomyopathy, noninvasive myocardial tissue characterization
is important. Previously, the echogenicity of the heart wallof patients with previous myocardial infarction and hypertrophic cardiomyopathy in the ultrasonic B- and M-mode
images was known to be high.1–6) However, quantitative
characterization of myocardial tissue has not yet beenrealized.
Integrated backscatter (IB) from the heart wall, which isable to measure the phenomenon in a region of a size lessthan the ultrasonic wavelength of about 500 m, is gaining
attention as a quantitative tissue characterization method.
The IB is obtained by averaging the ultrasonic scattering
power from a region in tissues. In previous studies, it was
found that IB from the myocardium exhibits cyclic variation
during one cardiac cycle,7–9) i.e., the magnitude decreases
during systole and increases during diastole. The magnitudeof such variation is reduced by ischemia.10) These results
suggest that the cyclic variation in ultrasound IB during
one cardiac cycle oﬀers potential for the evaluation of
myocardial contractility. Thus, analysis of the cyclic
variation of ultrasonic IB has been established as anoninvasive and sensitive method for evaluating intrinsic
left ventricular (LV) contractile performance and for
detecting myocardial viability.11–14)
Since there is large motion due to the heartbeat in theheart wall, in conventional measurement, the position of
the region of interest (ROI) for detecting IB is manuallyassigned in each frame during one cardiac cycle. Furthermore, the thickness of the heart wall changes duringcontraction and relaxation of the myocardium. However,the change in size of the ROI is completely ignored inconventional measurement of IB. Thus, it is diﬃcult toobtain IB from the same site during one cardiac cycle.
It is reported that a patient with myocardial infarction
shows a low CV in IB and a high baseline value of IB.
Naito et al. investigated the change in IB under doses ofE-mail address: kanai@ecei.tohoku.ac.jp

dobutamine and  blocker.15) They showed that CV in IB
was increased by dobutamine and decreased by  blocker.
They discussed that such changes in IB were caused by
the increased contractility of the myocardium caused by
dobutamine and the decreased contractility caused by blocker. Masuyama et al. showed that the CV of a patientwith hypertrophic cardiomyopathy was signiﬁcantly smaller
than that of a healthy subject.3) They mentioned that the
myocardial contractility of a patient with hypertrophic
cardiomyopathy was decreased by tangled myocardial ﬁber.
Furthermore, Hoyt et al. reported that there was a correlation between the amount of hydroxyproline, which is themain component of ﬁbrous tissue in the myocardium, andthe baseline value of IB.16)
To improve the spatial resolution in the estimation of the
myocardial displacement, Kanai et al. proposed the phased
tracking method, which enables the detection of small
vibrations in the heart wall.17) This method was applied tomultiple points preset in the LV wall along an ultrasonicbeam so that the spatial distribution of velocities at thosepoints is simultaneously obtained.18,19) Furthermore, thismethod was applied to other applications, such like themeasurements of heart wall vibrations induced by external
actuation20) and the strain waveform of the radial arterial
wall.21)
There are several studies on the measurement of IB withtracking of myocardial motion. Bai et al. measured cyclic
variation in IB by tracking myocardial motion using aspeckle tracking technique.22) They showed that the normal
myocardium and the infarcted myocardium can be diﬀerentiated by cyclic variation in IB measured by their method.
Sekioka et al. used a tracking method based on ultrasonicRF echoes for the measurement of IB.23) They mentionedthat diﬀerences between IBs of hearts of healthy subjects
and patients with myocardial infarction were enhanced bytracking myocardial motion. However, the temporal resolutions in these previous studies are not suﬃcient to detect thehigh-frequency variation in IB that is investigated in thepresent study. Therefore, the phased tracking method, which
can measure myocardial motion accurately at a hightemporal resolution, was used in the present study tomeasure IB from the myocardium.

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H. Shida et al.

In this study, by applying the phased tracking method,which estimates the displacement of an object with a highdegree of accuracy using the phase shift of the RF signal, an
ROI assigned in the heart wall along an ultrasonic beam isaccurately tracked. By setting the ROI between two adjacentpoints along the beam, the instantaneous position and thesize of the ROI corresponding to displacement and change inthickness of the heart wall are automatically determined.
Thus, it is possible to measure the IB in the same site of theheart wall in each frame with better time resolution andspatial resolution in the axial direction. Since the spatial
resolution and time resolution were signiﬁcantly improved,
rapidly varying components were observed in the IB signal.
Such rapidly varying components highly depend on thestrain rate of the heart wall and these components result fromthe interference between the ultrasonic waves reﬂected byscatterers. By applying the proposed method to an in vivo
experiment, the interference cycle of the IB signal was
calculated to estimate the rate of change in the thickness ofthe heart wall.

RV

RF acquisition area

shift with Δd /4=616 μm
Δd=2463 μm (layer thickness)v (x1i ;t )

RV
IVS

LV

IVS

Ao

i−th layerv (x2i ;t )LAultrasonic
beam

LVPW

(a)
(c)

(b) t =t 0

LV

ΔT =1/(frame rate)

t0
x1i
IVS

t0+ΔT t0+2ΔT
i−th layer

time

ΔD(t)

ROI

x2i
depth

integration

averaged
power

time
IB(t)

2. Principles
2.1 Detection of IB from the same site in the heart wall

Figure 1 illustrates the proposed method for calculating the
IB. At the time of electrocardiographic R-wave, N layerswith a thickness of d ¼ 2463 m were assigned in theinterventricular septum (IVS) from the right ventricular(RV) side to the left ventricular side along an ultrasonicbeam with intervals of d=4 ¼ 616 m and then, the IB was
calculated in each layer in one cardiac cycle. The thickness
d was determined from the duration of an ultrasonic pulse
transmitted from the ultrasonic probe. The IB signal IBi ðtÞ ofthe i-th layer from the RV surface (i ¼ 0) at time t is givenby24)
Z x2i ðtÞ1
IBi ðtÞ ¼ 10 log10
jzðt; Þj2 d;ð1ÞdðtÞ x1i ðtÞð2ÞdðtÞ ¼ x2i ðtÞ  x1i ðtÞ;where zðt; Þ is the quadrature demodulated signal of theultrasonic pulse scattered by the object at depth positionx ¼  at time t, and x1i ðtÞ and x2i ðtÞ are the top and bottom of
the i-th layer (i ¼ 0; 1; 2; . . . ; N  1), respectively.

time

Fig. 1. (Color online) (a) RF signal acquisition in the parasternallongitudinal-axis view of the LV. (b) Method of assigning layers along an
ultrasonic beam at t ¼ t0 . (c) Illustration of the proposed method for
calculating the IB by tracking the instantaneous position and thickness of the
ROI.

8
tÞ;
< SA ðt; n þ 1Þ ¼ cosð2f
 0

2ðd þ di Þ;
c0where f0 is the ultrasonic center frequency and c0 is theacoustic velocity. Thus, the phase diﬀerence i due to thechange in thickness di between two frames is given by: SB ðt; n þ 1Þ ¼ cos 2f0 t þ

i ¼ 2f0

In the present study, the interference cycle of the IB signal in
the time (frame) direction is estimated. When intramyocardial scatterers move in response to the changes in thicknessof the heart wall, the interference state of multiple scatteredwaves varies. If the distance between two scatterers is varies
owing to the change in thickness, the rate of change in the
distance of scatterers, i.e., the rate of change in thickness, isdetermined by estimating the cycle of the change in IB.
Figure 2(a) illustrates the case of two scatterers. Ultrasonicechoes from scatterer A and scatterer B in the n-th frameand (n þ 1)-th frame are given by8tÞ;< SA ðt; nÞ ¼ cosð2f
 0

2d
: SB ðt; nÞ ¼ cos 2f0 t þ
;
c0

ð3Þ

Therefore, the interference cycle Ti is given by substituting
i ¼ 2T =Ti as follows:
Ti ¼

2.2 Interference cycle of IB and rate of change inthickness

2di
:
c0

c0 T

:
2f0 dið4Þ

As shown in eq. (4) and Fig. 2(a), di =T indicates the rateof change in distance of scatterers, i.e., the rate of change inthickness. Then, the average rate of change in thickness vi ineach layer is given by
c0 1
 ;
ð5Þ
2f0 Tic0
 fi ;
ð6Þ
¼
2f0
where fi is the interference frequency. Also, the rate ofchange in thickness obtained by the phased tracking method
vip is given by25)vi ¼

vp;i ¼ jvðx2i ; tÞ  vðx1i ; tÞj;ð7Þ

where vðx2i ; tÞ and vðx1i ; tÞ are the velocities of the top andbottom of the i-th layer, respectively. The phased tracking
method requires two points along an ultrasonic beam to

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H. Shida et al.

(a)

(b)
IB(t)

SA (t ; n)Removing direct−current componenttime

SB (t ; n)rate of change
in thickness

scatterer
A

δd

δd

B

Cutting signals using window function
Adding zero points

using IB signal
using the phased
tracking method

DFT for the interference frequency(the interference cycle)

ΔdΔT

t0 t0+ΔT t0 +2ΔT

n+1 framentime
Evaluation of rate of change in thickness

Δ T =1/(frame rate)

Fig. 2. (Color online) (a) Relationship between interference cycle and rate of change in thickness in the case of two scatterers. (b) Illustration andschematic procedure of calculation of rate of change in thickness proposed in this study.

depthsystolediastole

10 mm

10 mm

apical
side

Ao

basal
side
LV
LA

7
6

LV

Ao

8
5

4

RV

RV

RV

3

47

IVS

38
IB 28
[dB]
18

1

2
beam number

LV(a) Tracking positionLA
LVPW
RF acquisition area(b) Color−coded IB signal
9Fig. 3. (Color online) Cross-sectional image of the left ventricle in the(c) ECG

long-axis view obtained by conventional echocardiography for a healthy
24-year-old male. The red arrows show the direction of the eight ultrasonicbeams used for calculation of IB in the IVS.

ROI position
RV sideMiddle of RV side and LV side
LV sideestimate the rate of change in thickness. In contrast, theinterference cycle of IB, which corresponds to the change inthickness, can be estimated using each single depth point. In
this study, the interference cycle was obtained by Fouriertransform in accordance with the process in Fig. 2(b). To
identify peaks in the frequency spectrum of the IB signal, it
is necessary to remove the direct-current component from IB
signals and zero points (total 512 points) were added to
improve the frequency resolution. Then, the rate of change
in thickness was calculated using the interference frequency
of IB and the phased tracking method.
3. In vivo Experimental Results

PCG

(d)

50
IB signal [dB]

45
40
35
30
25
20
15

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
time [s]Fig. 4. (Color online) In vivo experimental results for the IVS along

3.1 Discrimination of interference component from noise

Figure 3 shows a typical cross-sectional image (transthoracic parasternal longitudinal-axis view) of the heartobtained from a healthy 24-year-old male. The ﬁgure on
the right-hand side of Fig. 3 shows the RF acquisition area.
The RF data were acquired at a frame rate of 888 Hz using a
3.75-MHz sector-type probe of ultrasonic diagnostic equipment (ALOKA SSD-6500). The sampling frequency of the
RF signal was 15 MHz. Figure 4 shows IB signals of the RVside (red line), the middle (green line), and the LV side (blueline) of the IVS along beam 5. In Fig. 4, there is cyclic
variation in each ROI, which is the same as that reported
previously (the magnitude decreases during systole andincreases during diastole). During diastole, the myocardial
ﬁber was depressed and the orientation of the ﬁbers becamealmost parallel, and the incident angle of the ultrasoundbeam 5. (a) The tracking lines for RV side (red line), middle of IVS (greenline), and LV side (blue line) overlaid on the M-mode image.
(b) Color-coded image of IB signals. (c) ECG (red line) and PCG (blue line).
(d) IB signals for RV side (red line), middle of IVS (green line), and LV side
(blue line).

becomes perpendicular to almost all the ﬁbers. Thus, themagnitude of the integrated backscatter increased during
diastole. This is opposite in systole, i.e., there are various
ﬁber orientations. In addition to the conventional cyclic
variation, the rapidly varying components, which arethought to be due to interference between the ultrasonicwaves reﬂected by scatterers, are apparent during one
cardiac cycle. Figures 5(a)–5(c) are the enlarged views of IB
signals in diﬀerent periods (black dotted lines for each ROI
in Fig. 4). IB signals obtained by in vivo measurement

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H. Shida et al.

0.16

0.18

0.2

0.22

0.24

0.26

32
31
30

0.28

0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6

150

200

amplitude spectrum [dB]amplitude spectrum [dB]

100

−10

before spectal averaging (for 1 beat)after spectal averaging (the size of 9 beat)

−15
−20
−25
−30
−35

0

50

100

150

200

−10
before spectal averaging (for 1 beat)after spectal averaging (the size of 9 beat)

−15
−20
−25
−30
−35

0

50

100

150

frequency [Hz]

(d)

(e)

(f)

27.3

7.0
IB (avg.)
phased tracking method (avg.)
phased tracking method

23.4
19.5

4.0

15.6

3.0

11.7

2.0

7.8

1.0

3.9

0
0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36

time [s]

0

27.3

7.0
IB (avg.)
phased tracking method (avg.)
phased tracking method

6.0
5.0

23.4
19.5

4.0

15.6

3.0

11.7

2.0

7.8

1.0

3.9

0

0.16

0.18

0.2

0.22

0.24

0.26

0

0.28

time [s](g)rate of chnage in tihckness [mm/s]

frequency [Hz]interference frequency [Hz]frequency [Hz]

7.0

200

IB (avg.)
phased tracking method (avg.)
phased tracking method

6.0

27.3
23.4

5.0

19.5

4.0

15.6

3.0

11.7

2.0

7.8
3.9

1.0
0

0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6

time [s](h)0interference frequency [Hz]IB signal [dB]

26

33

(c)

−35

5.0

27

34

(b)

−30

6.0

28

35

(a)

−25

50

29

time [s]

−20

0

36

30

time [s]

−15

−40

37

31

time [s]before spectal averaging (for 1 beat)after spectal averaging (the size of 9 beat)

−10

32

25

rate of change in thickness [mm/s]−5IB signal [dB]

44
43
42
41
40
39
38
37
36
35
34
33
0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36

rate of change in thickness [mm/s]

rate of change in thickness [mm/s]

amplitude spectrum [dB]

IB signal [dB]

Jpn. J. Appl. Phys. 51 (2012) 07GF05(i)Fig. 5. (Color online) Measured rates of change in thickness obtained using interference frequency of IB signal within the period of black dotted line foreach ROI in Fig. 4. (a) Enlarged view of IB signal of RV side. (b) Enlarged view of IB signal of middle of IVS. (c) Enlarged view of IB signal of LV side.
(d) Amplitude spectrum of IB signal in (a). (e) Amplitude spectrum of IB signal in (b). (f ) Amplitude spectrum of IB signal in (c). (g) Average rate of change
in thickness in the RV side. (h) Average rate of change in thickness of middle of IVS. (i) Average rate of change in thickness in the LV side.

ECG

PCG

45
40
IB signal [dB]contained low-frequency and high-frequency components.
To examine these components, the spectra of IB signals
were averaged.
Figures 5(d)–5(f ) show the amplitude spectra obtained for
IB signals in Figs. 5(a)–5(c) by applying the DFT with
Hanning windows with lengths of 176 ms (RV side), 108 ms(middle of IVS), and 64 ms (LV side). In Figs. 5(d)–5(f ), thered line indicates the spectrum before averaging (for 1 beat)and the blue line indicates the spectrum after averaging (for9 beats). For each ROI, frequency components at over 50 Hz
were considered to be noise from the average spectrum.
Thus, the low-frequency components in Figs. 5(d)–5(f ) areconsidered to correspond to the interference component of
scatterers, i.e., the rate of change in thickness. From theaverage spectrum, the frequencies of peaks were calculated
to be 5.7 Hz (RV side), 8.7 Hz (middle of IVS), and 12.1 Hz(LV side) and these peaks were identiﬁed as interference
frequencies. Each interference frequency corresponds to thecycle indicated by the arrow on the IB signals in Figs. 5(a)–5(c). Figures 5(g)–5(i) show the average rate of change inthickness within the analysis period estimated using theinterference frequency of IB signals (red line) and thephased tracking method (blue line). The blue dotted line is
the instantaneous rate of change in thickness within theanalysis interval obtained by the phased tracking method. As
shown in Figs. 5(g)–5(i), the values obtained by the two

35
30
25
20
15

0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42
time [s]Fig. 6. (Color online) Enlarged view of IB signals in the period for
frequency analysis around second heart sound (90 ms).

methods were nearly equal. This indicates the possibility ofthe proposed method for estimating the rate of change inthickness using the IB signal.
3.2 Rates of change in thickness during same period andduring one cardiac cycle

Figure 6 shows an enlarged view of IB signals during the07GF05-4# 2012 The Japan Society of Applied Physics

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before spectal averaging (for 1 beat)after spectal averaging (the size of 9 beat)

−15
−20
−25
−30
50

100

150

200

−10
−15
−20
−25
−30

0

50

100

150

200

−5
before spectal averaging (for 1 beat)after spectal averaging (the size of 9 beat)

−10
−15
−20
−25
−30

0

50

100

150

frequency [Hz]frequency [Hz]

(a)

(b)

(c)

54.5
IB (avg.)
phased tracking
method (avg.)
phased tracking
method

12.0
10.0

46.8
39.0

8.0

31.2

6.0

23.4

4.0

15.6

2.0

7.8
0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42

0time [s]

14.0

54.5
IB (avg.)
phased tracking
method (avg.)
phased tracking
method

12.0
10.0

46.8
39.0

8.0

31.2

6.0

23.4

4.0

15.6

2.0

7.8

0

0

0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42

time [s](d)rate of change in thickness [mm/s]

frequency [Hz]

14.0

0

before spectal averaging (for 1 beat)after spectal averaging (the size of 9 beat)interference frequency [Hz]0rate of change in thickness [mm/s]

−35

0
−5

200

14.0

54.5
IB (avg.)
phased tracking
method (avg.)
phased tracking
method

12.0
10.0

46.8
39.0

8.0

31.2

6.0

23.4

4.0

15.6

2.0
0

7.8
0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42

time [s](e)0interference frequency [Hz]−5−10amplitude spectrum [dB]amplitude spectrum [dB]

H. Shida et al.

interference frequency [Hz]rate of change in thickness [mm/s]

amplitude spectrum [dB]

Jpn. J. Appl. Phys. 51 (2012) 07GF05

(f)

0.4

0.5

time [s]0.6

0.7

108 ms
180 ms
252 msphased tracking method

0.2

0.3

0.4

0.5

0.6

0.7

54.5
46.8
39.0
31.2
23.4
15.6
7.8
0

time [s]

(a)

14.0
12.0
10.0
8.0
6.0
4.0
2.0
0

108 ms
180 ms
252 msphased tracking method

0.2

0.3

0.4

0.5

0.6

0.7

time [s]

54.5
46.8
39.0
31.2
23.4
15.6
7.8
0

interference frequency [Hz]

0.3

14.0
12.0
10.0
8.0
6.0
4.0
2.0
0

rate of change in thickness [mm/s]

0.2

54.5
46.8
39.0
31.2
23.4
15.6
7.8
0

interference frequency [Hz]108 ms
180 ms
252 msphased tracking method

rate of change in thickness [mm/s]

14.0
12.0
10.0
8.0
6.0
4.0
2.0
0

interference frequency [Hz]rate of change in thickness [mm/s]

Fig. 7. (Color online) Measurement of rate of change in thickness obtained using interference frequency of IB signal in the period for frequency analysis
around second heart sound (90 ms). (a) Amplitude spectrum of IB signal in Fig. 6, RV side (red line). (b) Amplitude spectrum of IB signal of middle of IVS(green line). (c) Amplitude spectrum of IB signal in Fig. 5, LV side (blue line). (d) Average rate of change in thickness in the RV side. (e) Average rate ofchange in thickness of middle of IVS. (f ) Average rate of change in thickness in the LV side.

(c)

(b)

Fig. 8. (Color online) Comparison of instantaneous rates of change in thickness during one cardiac cycle using window lengths of 108 ms (red line),
180 ms (purple line), and 252 ms (green line) for frequency analysis. Instantaneous rate of change in thickness obtained by the phased tracking method isshown by the blue lines. (a) RV side. (b) Middle of IVS. (c) LV side.

period for frequency analysis around the second heart sound90 ms. Figures 7(a)–7(c) show the amplitude spectra of
IB signals obtained in Fig. 6 by applying the DFT with aHanning window with a length of 180 ms so that the distance
between scatterers in the myocardium largely varies and theinterference arises in each ROI, especially in the RV side.
From the average spectrum, the interference frequencies
were calculated at 5.2 Hz (RV side), 8.7 Hz (middle of IVS),
and 10.4 Hz (LV side). Each interference frequency corresponds to the cycle indicated by the arrow on the IB
signals in Fig. 6. Figures 7(d)–7(f ) show the average rates ofchange in thickness within the analysis period obtainedusing the interference frequency of IB signals (red line) andthe phased tracking method (blue line). The blue dotted lineis the instantaneous rate of change in thickness within theanalysis period obtained using the phased tracking method.
As described in the previous section, the values obtainedby the two methods are nearly equal, especially in the RV
side. Furthermore, the average values of rates of change inthickness within the analysis period are summarized inTable I. Average values of rates of change in thickness obtained using
two methods.

MethodIB signal

Phased tracking

ROI position

Rate of change in thickness(mm/s)

RV

1.34

Middle

2.23

LV

2.67

RV
Middle

0.79
1.14

LV

4.08

Table I. Both rates of change in thickness obtained by the
proposed method and the phased tracking method werelarger in the LV side than the RV side. Such a tendency is ingood agreement with previous reports.26) From these results,
the proposed method was shown to have potential for theestimation of the rate of change in thickness using theinterference cycle of the IB signal.

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1) A. K. Bhandari and N. C. Nanda: Am. J. Cardiol. 51 (1983) 817.
2) J. G. Miller, J. E. Perez, and B. E. Sobel: Prog. Cardiovasc. Dis. 28 (1985)

4. Discussion

As shown in the results in Figs. 7(d)–7(f ) and Table I, alarge window length is necessary when an ROI is assignedin the RV side to detect the interference between echos
from scatterers, which move in response to the change inthickness of the heart wall. That is, a large window length is
not indispensable for the LV side where the rate of change inthickness during one cardiac cycle is large. Also, myocardial
lateral motion cannot be neglected when such a long window
is used. Figure 8 shows the instantaneous rate of change inthickness during one cardiac cycle obtained using shorterand longer windows for frequency analysis. The results
obtained by both the proposed method and the phased
tracking method show a similar tendency (large change inthickness in the LV side). Also, it was found that theestimated values obtained by windows longer than 180 ms
are very close to that obtained by the phased tracking
method in the RV side and the middle of IVS. In contrast, thevalues obtained by windows shorter than 180 ms are very
close to that obtained by the phased tracking method in the
LV side. If the optimal window length is used in each frame
and ROI position, it might be possible to estimate the rate ofchange in thickness with a high degree of accuracy.

85.
3) T. Masuyama, F. S. Goar, T. Tye, G. Oppenheim, I. Schnittger, and R.

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4) J. Naito, T. Masuyama, T. Mano, H. Kondo, K. Yamamoto, R. Nagano, Y.

Doi, M. Hori, and T. Kamada: Am. Heart J. 131 (1996) 115.
5) M. R. Milunski, G. A. Mohr, K. A. Wear, B. E. Sobel, J. G. Miller, and

S. A. Wickline: J. Am. Coll. Cardiol. 14 (1989) 462.
6) J. Naito, T. Masuyama, K. Yamamoto, T. Mano, H. Kondo, R. Nagano, Y.

7)
8)
9)
10)
11)
12)
13)
14)

15)

5. Conclusion

16)

In this study, we proposed a method for estimation of therate of change in thickness using the IB signal. To examine
the low-frequency component and high-frequency component, the spectra of IB signals were averaged and theinterference components due to interference between theultrasonic waves reﬂected by scatterers, which move in
response to a change in thickness of the heart wall, were
found in addition to the conventional cyclic variation. Theinterference frequency calculated by DFT in the same period
reﬂected the well-known contractile and relaxant characteristics fairly well. Also, it was indicated that it might bepossible to estimate the rate of change in thickness with ahigh degree of accuracy if the optimal window length isselected for each frame and ROI position. These results
indicate that the proposed method have potential for theevaluation of the rate of change in thickness using theinterference cycle of the IB signal.

17)
18)
19)
20)
21)
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23)

24)
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26)

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