Jpn. J. Appl. Phys. Vol. 42 (2003) pp. 3239–3245
Part 1, No. 5B, May 2003
#2003 The Japan Society of Applied Physics

Measurement of Rapid Variation in Ultrasound Backscattering During Change
in Thickness of Tissue Phantom
Hiroshi K ANAI; y, Yoshiro K OIWAz, Shin’ichi K ATSUMATAy , Naoyuki I ZUMIy and Motonao T ANAKAx
Department of Electronic Engineering, Graduate School of Engineering, Tohoku University, Aramaki-aza-Aoba 05, Sendai 980-8579, Japan(Received November 18, 2002; accepted for publication March 12, 2003)

The cyclic variation in ultrasound integrated backscatter (IB) during one cardiac cycle oﬀers potential for evaluation of
myocardial contractility. Since there is large motion due to the heartbeat in the heart wall, in the conventional method, theposition of the region of interest (ROI) for calculating the IB is manually set for each timing during one heartbeat. Moreover,change in the size of the ROI during contraction and relaxation of the myocardium is not considered. In this paper, a new
method is proposed for automatic tracking of the position and the size of the ROI. Rapid components, which are detected byincreasing the spatial and time resolutions to 1 mm and 200 ms, respectively, highly depend on the instantaneous velocity of
the ROI. These components are the result of interference between the waves reﬂected by the ROI and those reﬂected byscatterers other than the ROI. By separately estimating the bias component, these interfering components which causeinterference are eliminated. By applying the proposed method to a sponge phantom, which was cyclically depressed in a watertank, and to the posterior wall of the heart of a healthy subject, the interference components were suﬃciently suppressed andthe IB signals were obtained with high spatial and time resolution. [DOI: 10.1143/JJAP.42.3239]
KEYWORDS: phased tracking method, integrated backscatter, sponge phantom, contraction and relaxation, myocardium
contractility, cyclic variation

1.

Introduction

One of the ultimate goals of medical ultrasonic research istissue characterization, that is, to provide supplemental
information describing the physical state of the tissue basedon a quantitative analysis of interactions between tissue andultrasound. In previous studies, it was found that ultrasoundintegrated backscatter (IB) from the myocardium exhibits
cyclic variation during one cardiac cycle1–3) and that themagnitude of such variation was reduced by ischemia.4)
These results suggest that the cyclic variation in ultrasoundIB during one cardiac cycle oﬀers potential for evaluation of
myocardial contractility. Thus, analysis of the cyclic variation of ultrasound IB has been established as a noninvasive
and sensitive method for evaluating intrinsic left ventricular(LV) contractile performance and for detecting myocardial
viability.5–8)
Since there is large motion due to the heartbeat in theheart wall, in conventional measurement, the position of theregion of interest (ROI) for detecting IB is manually set at
each timing during one heartbeat. Furthermore, the thicknessof the heart wall changes during contraction and relaxationof the myocardium. However, the change in size of the ROI
is completely ignored in conventional measurement.
In this paper, by introducing the phased tracking method,9,10) each displacement of multiple points, which are set
at intervals of 0.375 mm in the heart wall along an ultrasonicbeam, is accurately tracked. By setting the ROI between two
adjacent points, the instantaneous position and the size of the
ROI are automatically traced.
Since spatial resolution and time resolution were inE-mail address: hkanai@ecei.tohoku.ac.jp
Present address: Department of Electronic Engineering, Graduate Schoolof Engineering, Tohoku University Aramaki-aza-Aoba 05, Sendai 9808579, Japan.
zPresent address: First Department of Internal Medicine, Graduate Schoolof Medicine, Tohoku University Seiryou-machi, Aoba-ku, Sendai 9808574, Japan.
xPresent address: Tohoku Welfare Pension Hospital, Fukumuro 1-12-1,
Miyagino-ku, Sendai 983-8512, Japan.
ycreased to 1 mm and 200 ms, respectively, in this study,
components which rapidly varied were observed in the IB
signal for the ﬁrst time. Such rapidly varying components
highly depend on the speed of displacement of the ROI andthese components are the result of interference between the
waves reﬂected by the ROI and those reﬂected by the otherscatterers. Proposed herein is a method for eliminating these
rapid components in which by the bias component in thequadrature demodulated signal of the received radio frequency (RF) signal, is estimated.
By applying the proposed method to a sponge phantom,
which was cyclically depressed in a water tank, theinterference components were suﬃciently suppressed. Next,
the method was applied to the LV posterior wall of a healthy
subject in in vivo experiments. The IB signal was measured
with high time resolution and high spatial resolution, an
impossibility with the conventional method.
2.

Method for Maintaining the Same ROI in Detectionof the IB

2.1 Principle for tracking displacement in the heart wall
RF pulses with an angular-frequency of !0 ¼ 2f0 are
transmitted at a time interval of T from an ultrasonictransducer. The ultrasonic pulse, reﬂected by an object witha depth of x, is received by the same transducer. The phase
diﬀerence ðt; xÞ between the received signal yðt; xÞ and thesubsequently received signal yðx; t þ TÞ is given byðt; xÞ ¼ ðx; t þ TÞ
2!0xðtÞ;¼c0ðt; xÞ
ð2:1Þ

where ðt; xÞ is the phase of the received signal yðt; xÞ,xðtÞ ¼ xðt þ TÞ xðtÞ is the displacement of the object
during the period T from a time t, and c0 is the acoustic
velocity in the human body. By dividing the movement x
by the period T, the average velocity vðt þ T
2 Þ of theobject during the period T is given by3239

Jpn. J. Appl. Phys. Vol. 42 (2003) Pt. 1, No. 5Bt+∆T t+2∆Ttsquared magnitudeof demodulated signal

ð2:2Þ

By moving the depth of the object along the direction of theultrasonic beam based on the resultant object depth bxðt þTÞ by bvðt þ TÞT,the
displacementoftheobjectis2
tracked, and then the velocity signal bvðt þ T
Þonthe
tracked2large motion can be accurately estimated.9) This procedure iscalled the phased tracking method.
The LV wall shows large motion with an amplitude ofabout 10 mm during the cardiac cycle, and the LV wallshows periodic thickening and thinning along with myocardial contraction and relaxation, the magnitude of which isabout 30% of the thickness in healthy subjects.10)
2.2 IB detection of the same ROI
The diﬀerence between position bxi ðtÞ of the ith point andposition b
xiþ1 ðtÞ of the ði þ 1Þth point set along an ultrasonicbeam shows the local thickness at every instant of time
during one cardiac cycle, where bxiþ1 ðtÞ > b
xi ðtÞ. Let us deﬁnei-th ROI as the region between these two positions b
xi ðtÞ andb
xiþ1 ðtÞ as shown in Fig. 1. Thus, the IB value, IBi ðtÞ, of the ith ROI is given byZb
xiþ1 ðtÞ
1
IBi ðtÞ ¼ 10 log10
jzðt; xÞj2 dx;ð2:4Þ
bxiþ1 ðtÞ bxi ðtÞ bxi ðtÞ
½dBi−th pointi−th ROI(i+1)th point

IB i(t)time
Fig. 1. Illustration of the proposed method for calculating the IB bytracking the instantaneous position and thickness of the ROI.

explained below.
First, an optimal case is considered, that is, the received
signal yðt; xÞ contains only the ultrasonic pulse y0 ðt; xÞreﬂected by the scatterers in the ROI at position x. To
describe the displacement of the ROI, the quadrature
demodulated signal zðt; xÞ of yðt; xÞ is described by
zðt; xÞ ¼ z0 expfjðtÞg, where ðt; xÞ denotes the phase delay
due to the two-way transmission of the ultrasonic pulse fromultrasonicprobe

stationary object(scatterers)0y (t;x)

)

t;x
y (1

where zðt; xÞ is the quadrature demodulated signal of theultrasonic pulse yðt; xÞ reﬂected by the object at position x attime t. Thus, the spatially averaged squared magnitude of thequadrature demodulated signal is normalized by the instantaneous thickness b
xiþ1 ðtÞ bxi ðtÞ of the i-th ROI as shown in
Fig. 1.
2.3 Cause of the rapid change components in IB signals
In actual measurement, the received signal yðt; xÞ hassome components y1 ðt; xÞ other than the ultrasonic pulse
y0 ðt; xÞ reﬂected by the ROI. These components, y1 ðt; xÞ, arethe result of the ultrasonic pulse reﬂected at the other points
due to the side lobe or the grating lobe of the ultrasonictransducer as illustrated in Fig. 2. These components,y1 ðt; xÞ, interfere with the ultrasonic pulse y0 ðt; xÞ reﬂected
at the ROI. The ROI is set in the heart wall and has large
motion due to the heartbeat. On the other hand, it can beassumed that the position of the other points do not change
so much. In this case, the IB has rapid change components as

time

integrationc xÞ is accurately determined
where the phase diﬀerence ðt;by the constraint least-squares approach based on thecomplex cross-correlation between the quadrature demodulated signals yðt; xÞ and yðx; t þ TÞ for suppressing noise
components under the constraint that the signal waveform isinvariant during T and that only the signal phase canchange.9) By multiplying the resultant velocity bvðt þ T2 Þ bythe period T, the next depth bxðt þ TÞ is estimated by


T
b
T:
ð2:3Þ
xðt þ TÞ ¼ bxðtÞ þ b
v tþ
2

depth



T
xðtÞ
b
¼
v tþ
2
T
c xÞ
c0 
ðt;
¼
;
2!0 T

H. KANAI et al.

averaged
power

3240

moving object(sponge or heart wall)Fig. 2. Interference between the ultrasonic pulse reﬂected by a moving
object and that reﬂected by scatterers in a stationary object due to the side
lobe or the grating lobe of the ultrasonic probe.

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H. KANAI et al.

the ultrasonic probe to the object at position xðtÞ and time t,
and z0 is the amplitude of the received pulse. When the ROI
follows the position of the same object in the heart wall as
illustrated in Fig. 2 and the change in attenuation can be
negligible for a short period, z0 can be assumed to beconstant. Thus, the magnitude of the quadrature demodulated signal, jzðt; xÞj, in eq. (2:4) keeps the same value,
namely,magnitude z 0ð2:5Þ

which shows that the quadrature demodulated signal zðt; xÞrotates around the circumference of the circle the circle witha radius of z0 as illustrated in Fig. 3(a). The center of thecircle coincides with the origin.
Secondly, when the received signal yðt; xÞ contains theultrasonic pulse y1 ðt; xÞ reﬂected by the other points as inFig. 2, let us roughly describe the component as z1 andassume that it does not change for a short period of time.
Thus, the quadrature demodulated component zðt; xÞ of thereceived signal yðt; xÞ is described by zðt; xÞ ¼
z0 expfjðtÞg þ z1 . Dividing z1 into the real part zR1 and theimaginary part zI1 , the magnitude jzðt; xÞj is given by

½dB

0

(a)
−1

+1

0

+1

imaginary part

apparent magnitude

ð2:6Þ

2.4 Correction of rapid change components in IB signals
By assuming that the position of the other point does notchange, we can estimate component z1 as follows. We set theregion Rz1 in the lumen close to the surface of the wall of theobject along an ultrasonic beam. The component z1 isestimated from the quadrature demodulated signal zðt; xÞaveraged over the set region Rz1 . In the lumen, the received
signal yðt; xÞ, reﬂected by the red blood cell scatterers has
almost the same phase value in the quadrature demodulated
signal zðt; xÞ over Rz1 . Then, the IB value IBi ðtÞ of the i-th
ROI in eq. (2:4) is correctly obtained after the estimatedbiased component b
z1 is subtracted from the quadrature
demodulated signal zðt; xÞ at the ROI as follows:Zbxiþ1 ðtÞ
1
jzðt; xÞ b
z1 j2 dx
IBi ðtÞ ¼ 10 log10
ð2:7Þ
b
xiþ1 ðtÞ bxi ðtÞ bxi ðtÞ

θ (t)

0

−1

jzðt; xÞj ¼ jz0 expfjðt; xÞg þ z1 jqﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ¼ ðz0 cos ðt; xÞ þ zR1 Þ2 þ ðz0 sin ðt; xÞ þ zI1 Þ2 :The center of the circle shifts from the origin by the ‘‘bias’’component z1 ¼ ðzR1 ; zI1 Þ as illustrated in Fig. 3(b). Thus, themagnitude jzðt; xÞj of the received signal, which coincides
with the distance of the point from the origin, changes
according to the rotation of the point around the circumference of the circle. The displacement of the ROI by the wave
length  of the ultrasound with a frequency of f0 Hz
corresponds to the rotation of the point by 2 radian in thecircle. In the heart wall, during one cardiac cycle, thedisplacement is roughly 10 mm, which corresponds to
10 mm 2 2f0 =c0  49 2 radian, where f0 ¼
3:75 MHz. Therefore, the components with rapid change
occur at the magnitude of zðt; xÞ of eq. (2:4). Thisphenomenon occurs not only for quadrature demodulated
signal zðt; xÞ but also for the original RF signal yðt; xÞ.

z(t;x)+1

imaginary part

jzðt; xÞj ¼ z0 ;

3241

θ(t)
bias

0

z1
0

−1
(b)
−1

bias
0
real part+1

Fig. 3. Magnitude and phase of the quadrature demodulated signal for thecase without bias component (a) and with bias component (b).

3.

Basic Experiments with Sponge Phantoms

3.1 Experimental setup and tracking results
The above method was applied to a sponge phantom madeof polyurethane in a water tank as shown in Fig. 4.
The macroscopic and the microscopic images of the
sponge phantom are shown in Fig. 5. The sponge was set
under an ultrasonic probe and was manually depressed byabout 5 mm at 1-second intervals. A sector-type ultrasonicprobe with a frequency of 3.75 MHz was employed. Using
conventional ultrasound diagnostic equipment (ToshibaSSH-140A), an ultrasonic pulse was transmitted. The pulse
repetition frequency was 4.5 kHz. The pulse reﬂected by thescatterers in the sponge was received by the same probe.
After being ampliﬁed and quadrature demodulated, theresultant signal zðt; xÞ was A/D converted at a sampling
frequency of 10 MHz.
Using a hydrophone, the duration time t of the radiatedultrasonic pulse at the focal area was determined to be about
1,330 ns, which corresponds to a distance of about
1; 500t=2 ¼ 1 mm in depth direction. Thus, the lengthof the ROI along the ultrasonic beam was set at 1.05 mm in
the following experiments.
Figure 6 shows the results for the sponge. The 14 red lines

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H. KANAI et al.

ultrasonicdiagnostic
equipment
demodulated
signaltiming pulse

ultrasonicprobe

A/D converter
GPIB

spongeworkstation
Fig. 4. Experimental setup for repeatedly depressing a sponge phantom in a water tank.

Fig. 5. top: Sponge phantom. bottom: The microscopic view.

in the sponge area of Fig. 6(a) show the tracking results
overlaid on the M-mode, which was reconstructed from themagnitude of the received quadrature demodulated signals.
The amplitude of the change in thickness during one cycle
was about 5 mm. Figure 6(b) shows the timing pulses of thecontraction of the sponge. Figure 6(c) shows the 14 velocity
signals at the 14 points which were followed by the tracking
lines in Fig. 6(a). The maximum velocity value is similar tothat in the actual human heart.9) Figure 6(d) shows the speed

Fig. 6. Tracking results for the sponge. (a) The 14 tracking lines overlaid
on the M-mode image. (b) Timing pulses resulting from depression of the
sponge. (c) The 14 velocity signals on the 14 tracking lines in (a). (d)Speed of the change in thickness of 13 layers, each of which was theregion between two adjacent tracking lines. (e) The change in thickness ofthe 13 layers. (f) The amplitude of the received signal along the ﬁrst
tracking line near the surface of the sponge and the averaged amplitude of
the biased component z1 obtained in the assigned region Rz1 . (g) The
phase component of the received signal along the ﬁrst tracking line near
the surface of the sponge. (h) The phase component of the biased
component z1 .

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3243

Fig. 7. IB signals for each of the 13 layers for the Sponge. (a) before correction, (b) after correction.

of the change in thickness of the 13 layers (ROI), each ofwhich was deﬁned as the region between the two adjacent
tracking lines in Fig. 6(a). Figure 6(e) shows the change inthickness of the 13 layers.
Figure 6(f) shows the amplitude of the received signal
along the ﬁrst tracking line near the surface of the sponge
and the averaged amplitude of the biased component z1
obtained in the assigned region Rz1 in top of Fig. 6(a).
Though the former component changed rapidly during one
cycle, the latter bias component z1 was almost constant.
Figures 6(g) and 6(h) show the phase component of thereceived signal along the ﬁrst tracking line near the surfaceof the sponge and that of the biased component z1 . Also forthese components, the former component changed rapidly
during one cycle but the latter bias component was almost
constant. Thus, the correlation between the estimated biased
component z1 and the movement of the sponge wasnegligible.
3.2 IB signals and their correction
The left-hand side of Fig. 7 shows the IB signal obtainedby eq. (2:4) for each of the 13 layers in Fig. 6(a). There wererapid change components from 10 Hz to 80 Hz observed at
the times of measurement when the velocity has a large
value in Fig. 6(c). The period (D) from 0.2 second to 0.5
second corresponds to the diastole in the heart wall and theperiod (S) from 0.7 second to 1.0 second corresponds to thesystole. By comparing the IB values between the period (S)and the period (D), the envelope of the IB values decreased
for both period (S) at from the ﬁrst layer to the second layer
and from the 4th layer to 5th layer. This phenomenon
corresponds to the well-known cyclic variation during one
cardiac cycle.11–13) That is, during diastole the ﬁber in the
sponge or intercelluar cement in the myocardium wasdepressed and the orientation of the ﬁbers became almost
parallel. Then, the incident angle of the ultrasound becomes
perpendicular to almost all the ﬁbers. Thus, the magnitude of
the backscatter increased during diastole. For the otherlayers, however, these cyclic variation was not observed.
By applying the proposed correction in eq. (2:7) to thesame quadrature demodulated signal using the biased
component z1 of Fig. 6(f), the corrected results of the IB
signals are shown in the right-hand side of Fig. 7. Almost all
the rapid change components in the left-hand side of Fig. 7
were successfully eliminated by the proposed method. Thus,
the assumed reason for the occurrence of the interference in
the IB is found to be valid.
The ﬁne M-mode images jzðt; xÞj before and after thecorrection are shown in Figs. 8(a) and 8(b), respectively. In
Fig. 8(a), rapid change components are seen at themeasurement times when the object has large velocity. By
the correction, however, these components were eliminatedin almost all the layers as shown in Fig. 8(b).

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Fig. 8. Fine M-mode images for Sponge (A). (a) before correction, (b) after correction.

4.

In vivo Experiment for Heart Wall

The same method was applied to the LV posterior wall of
the heart of a healthy male subject. The B-mode crosssectional image is shown in Fig. 9. The employed frequencyof the ultrasound was 3.75 MHz. The pulse repetition
frequency was 4.5 kHz. The IB signals on the ﬁne M-mode
images before and after correction are respectively shown in
Figs. 10(a) and 10(b). Figures 11(a) and 11(b) show the IB

Fig. 9. Cross-sectional B-mode image of the heart of a healthy malesubject.

signal in each layer of the wall before and after correction,
respectively.
In Figs. 10(a) and 11(a), rapid change components areapparent, especially at the beginning of the ejection period,

Fig. 10. M-mode images of the LV posterior wall. left: before correction,right: after correction.

Jpn. J. Appl. Phys. Vol. 42 (2003) Pt. 1, No. 5B

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3245

Fig. 11. IB signals for each of the 7 layers for the LV posterior wall. upper: before correction, lower: after correction.

in the rapid ﬁlling phase, and in the slow ﬁlling phase. By
the correction, almost all these rapid components were
eliminated in Figs. 10(b) and 11(b). In the region close to theendocardium, cyclic variation occurred, that is, the IB
increased during diastole by about 10 dB from the IB values
during systole.
5.

Conclusions

In this paper, a method has been proposed to automatically track the position and the size of the ROI for
calculating IB with high spatial and time resolution. By
setting the ROI between two adjacent points, the position
and the size of the ROI were automatically traced. Since
spatial resolution and time resolution were increased to
1 mm and 200 ms, respectively, rapid variation components
appeared in the IB signal for the ﬁrst time. Such rapid
components highly depend on the speed of change inthickness and these components are the result of interference
among the waves reﬂected by scatterers other than the
myocardium in the ROI. Thus, we have proposed a method
for eliminating these rapid components by estimating thecomplex value of the bias components in the quadrature
demodulated signal.
By applying the proposed method to a sponge phantom,
the interference components were suﬃciently suppressed.
Next, the method was applied to the LV posterior wall of ahealthy subject. The IB signal was measured with high time
resolution and high spatial resolution, indicating that thismethod has potential for diagnosis of the vulnerability of theregional heart muscle.
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