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ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 44, no. 4, july 1997

Noninvasive Evaluation of Local Myocardial
Thickening and Its Color-Coded Imaging
Hiroshi Kanai, Member, IEEE, Hideyuki Hasegawa, Noriyoshi Chubachi, Member, IEEE,
Yoshiro Koiwa, and Motonao Tanaka
Abstract—For the noninvasive diagnosis of heart disease
based on the acoustic characteristics of the heart muscle,
we have developed a new method for accurately tracking
the movement of the heart wall. By this method, a velocity signal of the heart wall with a small amplitude of lessthan 10 m on the motion resulting from a heartbeat withlarge amplitude of 10 mm can be successfully detected with
sufficient reproducibility in the frequency range up to several hundred Hertz continuously for periods of about 10
heartbeats. In this paper, the method is applied to multiple points preset in the left ventricular (LV) wall along theultrasonic beam so that the spatial (depth) distributionsof the velocity at these points are simultaneously obtained.
The motion of the heart wall is divided into the following two components: parallel global motion of the heart walland the change in myocardial layer thickening at each depth
across the LV wall during myocardial contraction/relaxation.
The latter component is superimposed on the M (motion)mode image using a color code to map contraction as red
and expansion as blue. By preliminary human studies, theprinciple of the method proposed in this paper is verified
and the frequency band of the components generated bythickening and/or thinning in the myocardium is identified.
This new approach offers potential for research on noninvasive acoustical diagnosis of myocardial local motility, thatis, the myocardial layer function at each depth in the ventricular wall.

I. Introduction
e herein consider the detection of velocity signals {v(xi ; t)} at multiple points {i} preset in the LV
wall as illustrated in Fig. 1(a) using ultrasound from thechest wall, where the symbol {·} denotes the set employedin this paper. The instantaneous position in the depth direction of the ith point set in the LV wall is denoted byxi (t) as shown in Fig. 1(b). The component of the motion parallel to the ultrasonic beam is shown in Fig. 1(c).
The parallel components at all points along the ultrasonicbeam in Fig. 1(c) are the same in phase and magnitude if
the beam is perpendicular to the heart wall. The LV wall

W

Manuscript received June 3, 1996; accepted December 16, 1996.
This work was supported in part by a Grant-in-Aid for Scientific
Research from the Ministry of Education, Science and Culture ofJapan.
H. Kanai, H. Hasegawa, and N. Chubachi are with the
Department of Electrical Engineering, Faculty of Engineering., Tohoku University, Sendai 980-77, Japan (e-mail:hkanai@chubachi.ecei.tohoku.ac.jp).
Y. Koiwa is with the First Department of Internal Medicine, Schoolof Medicine, Tohoku University, Sendai 980-77, Japan.
M. Tanaka is with the Tohoku Welfare Pension Hospital, Takasago
10, Fukumuro, Miyagino-ku, Sendai 983, Japan.

Fig. 1. An illustration explaining the process of the evaluation of thelocal change in thickness during myocardial contraction/relaxation
based on noninvasive detection of velocity signals {v(xi ; t)} and theinstantaneous positions {xi (t)} of multiple N points {i} in the heartwall. (a): Cross-sectional image of the heart wall. (b): Tracking results {xi (t)} for multiple N points {i} in the heart wall, shown in thesame form as in the M-mode image. xi (t) shows the instantaneous
position in the depth direction of the ith point preset in the heartwall, where i = 1, 2, . . . , N . (c) and (d): Tracking results {xi (t)} are
divided into the parallel motion x1 (t) in (c) and the local change inthickness {xi (t) − x1 (t)} during myocardial contraction/relaxationin (d). From the latter spatial distribution, the instantaneous local change in thickness, which corresponds to the myocardial local
motility, is evaluated and displayed in a color-coded image in thispaper.

motion during the cardiac cycle is much larger in magnitude compared with the thickness change. The LV wallshows periodic thickening and thinning along with myocardial contraction and relaxation as illustrated in Figs. 1(b)and (d). The difference between position xi (t) of the ith
point and position xi+1 (t) of the (i + 1)th point shows the
local thickness at every instant of time during one cardiac
cycle as shown in Fig. 1(d). The thickness change corresponds to the local motility of the myocardial layer acrossthe LV wall, possibly an essential diagnostic tool for heartdiseases.
To establish this noninvasive method for the local characteristics across the LV wall using ultrasound, accuracy

0885–3010/97$10.00 c 1997 IEEEkanai et al.: myocardial thickening and color-coded imaging

753

required in the simultaneous measurement of the instantaneous positions {xi (t)} of the multiple points {i} in theheart wall is estimated as follows. For the interventricular
septum (IVS), for example, the thickness is about 10 mm
for a normal young adult and the change in thickness isapproximately 1 mm to 3 mm during one cardiac cycle [1].
Thus, when the distance between points (i) and (i + 1) is0.75 mm, the minimum value of the thickness change between these points is approximately 75 µm. For the evaluation of local myocardial motility, therefore, 10 µm is
employed as the necessary spatial resolution in the measurement of instantaneous position. If the velocity signalv(xi ; t) of the ith preset point is detected based on thepulse Doppler method, necessary accuracy of the velocity
measurement is about 10 µm/200 µs = 0.05 m/s when thepulse repetition frequency (PRF) of the transmission-pulse
train is 5 kHz (= 1/200 µs). If the equivalent sampling period of the velocity signal v(xi ; t) is longer than 200 µs as
in the standard color Doppler system, for example, moreaccurate velocity measurement is required. Since there ismotion with large amplitude (about ±10 mm) caused by
the heartbeat as described above, moreover, the dynamic
range required in the measurement of the displacement isabout 1000 (= 10 mm/10 µm) = 60 dB in amplitude.
M-mode echocardiography offers an advantage in critically looking at the motion pattern of the left ventricle because of the increased frequency of sampling. However, its
spatial resolution along the ultrasonic beam is limited to a
few wavelengths, namely, only up to 1 mm for ultrasoundof 3 MHz. Moreover, to detect the displacement of point(i) as waveform as shown in Fig. 1(b) to be analyzed, it isnecessary to accurately identify its instantaneous positionxi (t) and to trace the resultant displacement. However,this is not easily realized in M-mode echocardiography. On
the other hand, numerous elaborate techniques have been
proposed for noninvasive measurement of the velocity ofthe blood flow in the heart or the arteries based on the
Doppler effect [2]–[11]. Moreover, several methods, including the PLL techniques, have been developed to measurechanges in the diameter of the arterial walls by tracking arterial wall displacement including only low frequency components with small amplitudes [12]–[31]. However, transcutaneous and accurate detection of the velocity signal on orin the heart wall has not yet been established.
We have proposed, therefore, a noninvasive transcutaneous method for detecting small velocity signals on thesurface of the heart wall [1], [32]. By calculating the constraint cross-correlation function between the sequentially
received echoes, the phase change caused by displacementof the ith preset point during the pulse repetition period ∆T is accurately determined and the average velocityv(xi ; t) during the period is obtained. By adding the product of v(xi ; t) and ∆T to the previous object position xi (t),the next position xi (t + ∆T ) is estimated. The detectedvelocity signal shows rapid motion of the heart wall including high frequency components with small amplitudes,
which are difficult to recognize by M-mode echocardiography. The validity of the proposed method has been con-firmed by experiments using a water tank and has been
applied to the in vivo detection of small velocity signals,
with sufficient reproducibility, on the wall of the humanheart [1]. Spectrum analysis was first applied to the resultant noninvasively detected signals to show the possibilityof acoustic diagnosis of the heart wall [1]. However, it corresponds to the global evaluation of the heart wall because
the detected velocity signals have not been divided into theparallel and thickness change components, and the lattercomponent is much less than the former one.
In this paper, the method is applied to multiple points
preset along an ultrasonic beam in the LV wall so that the
instantaneous object positions {xi (t)} and the velocity signals {v(xi ; t)} are obtained for these multiple points {i}in the LV wall. From the spatial distributions of {xi (t)}and {v(xi ; t)} in the direction of depth, the motion of the
LV wall is divided into the parallel component x1 (t) as
shown in Fig. 1(c) and the thickness change components{xi (t)−xi−1 (t)} during myocardial contraction/relaxation,
as shown in Fig. 1(d). From the latter component, the spatial distribution of the normalized local change in thicknessof the heart wall is obtained and is superimposed on the Mmode image using a color code. The principle is confirmedby the preliminary in vivo experiments herein reported.
By applying spectrum analysis to the velocity signals, thefrequency band for the component due to the myocardial
thickening and thinning is identified.

II. Principle of Accurate Measurement of
Instantaneous Position and Velocity
in the Myocardium
From observation of the standard echo cardiography,
it can be assumed that there are many objects along theultrasonic beam in the heart wall which reflect the transmitted ultrasonic pulse. Thus, we manually preset multiple
N points {i} in the heart wall at a time t0 in one cardiac
cycle by referring to the M-mode image. In this paper, we
assume that each point of {i} has a velocity component
which is parallel to the direction of this beam if the direction and position of the ultrasonic beam are appropriately
selected so that it is perpendicular to the wall of the heart
during the cardiac cycle. The principle of the accurate detection of the instantaneous positions {xi (t)} and velocity
signals {v(xi ; t)} of multiple points {i} in the heart wall isbriefly described as follows by referring to [1].
A. Measurement of Object Velocity v(xi ; t)RF pulses with angular-frequency ω0 = 2πf0 are transmitted at a time interval of ∆T from an ultrasonic transducer on the chest surface as illustrated in Fig. 2. Defining
the acoustic velocity as c0 , the instantaneous distance ofa object point (i) from the ultrasonic transducer is denoted by xi (t) = c0 · τi (t), where τi (t) is the instantaneous
period required for one-way transmission from the ultrasonic transducer to the object (i). The ultrasonic pulse

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ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 44, no. 4, july 1997

during the period ∆T around the time t+∆T /2 is given by
the phase difference ∆θ(xi ; t) between the successively received analytic signals y(xi ; t) and y(xi ; t + ∆T ) as follows
[11]:


∆T
∆xi (t)vb xi ; t +=2∆T∆θ(xi ; t)
. [m/s]= c0 ·
2ω0 · ∆T

(2)

B. Accurate Determination of the Phase Change ∆θ(xi ; t)Fig. 2. Schematic representation of the principle of the transcutaneous detection of a velocity signal v(xi , t) and the instantaneous
position xi (t) of the ith point in the heart wall using pulsed ultrasound from the chest wall.

Since it is essential to accurately determine the phasechange ∆θ(xi ; t) of (2) during the period ∆T , the following complex correlation is introduced in the determination
procedure of the movement, δx , of the object position xi (t)from the data of the preceding section during the period∆T .
Based on the least squares method, we define the normalized mean squared difference between the analytic signal y(xi + δx ; t + ∆T ) and the preceding signal y(xi ; t) by
αn (βn ; δx ),αn (βn ; δx )reflected by the object (i) is received by the same ultrasonic transducer. The output signal, z(t), is amplified andquadrature-demodulation is applied to the signal. The resultant in-phase and quadrature signals are simultaneously
A/D converted at a sampling period of TS , and these two
signals are combined into a complex signal, which is termed
an analytic signal. The analytic signal is then separated
into the response signals {y(xi ; t)} for each transmitted
pulse, where xi (t) and its simple expression xi denote thedepth of the object (i) from the ultrasonic transducer. The
spatial resolution ∆xS in the depth direction is equal to
TS · c0 /2 as shown in Fig. 2.
The phase θ(xi ; t) of the resultant sectional analytic
signal y(xi ; t) is given by the angular frequency ω0 multiplied by twice the delay time τi (t) in the one-way propagation from the ultrasonic transducer to the object. Thus,
the phase difference ∆θ(xi ; t) between the analytic signalsy(xi ; t) and y(xi ; t + ∆T ) of the received signals for the
successively transmitted pulses in the interval ∆T is givenby∆θ(xi ; t) = θ(xi ; t + ∆T ) − θ(xi ; t)
= 2ω0 {τi (t + ∆T ) − τi (t)}2ω0=∆xi (t),c0(1)where ∆xi (t) = xi (t + ∆T ) − xi (t) is the movement of theobject (i) in the period ∆T after a time t, where it can beassumed that the received interval almost coincides withthe transmitted interval ∆T of the ultrasonic RF pulses.
By dividing the movement ∆xi (t) by the period ∆T , theaverage velocity, denoted by vb(xi ; t + ∆T2 ), of the object

xi (t)+∆xP=

2|y(x + δx ; t + ∆T ) − βn (δx ; xi ; t)y(x; t)|x=xi (t)−∆xxi (t)+∆xP
x=xi (t)−∆x

1
2

n
o
2
2
|y(x + δx ; t + ∆T )| + |y(x; t)|,where δx is the movement, to be determined, of the object i during the period ∆T of the consecutive echoes andβn (δx ; xi ; t) is the average change from the analytic signaly(x; t) to y(x + δx ; t + ∆T ) around xi (t) and is a function of δx , xi (t), and t. The range from xi (t) − ∆x to
xi (t) + ∆x around the previous object-position xi (t) is
the period where the above difference is evaluated and therange 2∆x corresponds to the length of the RF pulse transmitted from the ultrasonic transducer. The denominatorof (3) shows the average power of these analytic signals
around xi (t), which normalizes the mean squared difference of the numerator.
From the theoretical consideration [1], the optimum
value of βn by which the minimum of αn (βn ; δx ) is given
coincides with the βn which maximizes the magnitude of
the standard complex cross-correlation function betweeny(x; t) and y(x; t + ∆T ) in the range around xi (t).
When the received complex signals y(x; t) and y(x; t +∆t) are described by the damped sinusoidal signals, however, the above standard cross-correlation procedure does
not uniquely determine the optimum movement δx ofthe signal y(x; t + ∆t) from y(x; t) as theoretically described in [1]. To solve the above problem, by restricting
the magnitude of βn (δx ; xi ; t) in (3) to one and replacing βn (δx ; xi ; t) by exp(j∆θ(δx ; xi ; t)), we redefine the normalized mean squared difference α(∆θ; δx ) of (3) between

kanai et al.: myocardial thickening and color-coded imaging

y(xi + δx ; t + ∆T ) and y(xi ; t) by α(∆θ; δx ):in the above procedure because the instantaneous velocityv(xi ; t) is given by the phase difference ∆θ(xi ; t) in (2).
Thus, accurate tracking of the object is realized by thismethod, which is confirmed by the experiments in Section V.

α(∆θ; δx )xi (t)+∆xP=y(x + δx ; t + ∆T ) − ej∆θ(δx ;xi ;t) y(x; t)x=xi (t)−∆xxi (t)+∆xP
x=xi (t)−∆x

1
2

2

n
o
2
2
|y(x + δx ; t + ∆T )| + |y(x; t)|,III. Principle of the Measurement of Thickness
Change in the Myocardium

where ∆θ(δx ; xi ; t) is the phase change from y(x; t) to y(x+δx ; t + ∆T ) around xi (t) and is a function of δx , xi (t), andt. The minimization of α(∆θ; δx ) is achieved by:xi (t)+∆xPc =exp(j ∆θ)

x=xi (t)−∆xxi (t)+∆xPy ∗ (x; t) · y(x + δx ; t + ∆T ).
y ∗ (x; t) · y(x + δ ; t + ∆T ) (3)xx=xi (t)−∆xc the minimum αM IN (δx ) of
For this value of exp(j ∆θ),c is uniquely given. By incα(∆θ; δx ) with respect to ∆θ
troducing the restriction, a solution different from thecomplex cross-correlation function derived from the nonrestricted definition in (3) is obtained [1]. From the phasec δbx ; xi ; t) and δbx by which minimization ofchange ∆θ(α(∆θ; δx ) in (3) is achieved, the average velocity in (2)is given by:
c δbx ; xi ; t)∆T∆θ(
vb xi ; t += c0 ·. [m/s]22ω0 · ∆T

755

(4)

C. Tracking the Object Position xi (t)The position xi (t) of the object (i) in the heart wallchanges by more than 10 mm due to the heartbeat in one
cardiac cycle. It is, therefore, necessary to accurately track
the instantaneous object position xi (t) in order to estimate
the velocity signal v(xi ; t) of the object (i). For this purpose, by multiplying the velocity estimate vb(xi ; t + ∆T2 ) of(4) by the period ∆T , the next object position xbi (t + ∆T )is estimated by:∆T
xbi (t + ∆T ) = xbi (t) + vb xi ; t +· ∆T. [m]2(5)
Thus, the resultant
object position xbi (t) and the velocity

vb xi ; t + ∆Taresimultaneously
determined.
2
The quadrature-demodulated signals are A/D converted at a sampling interval of TS . When the velocity
is assumed to be 5 mm/s, for example, and the time interval ∆T of the transmission of the RF pulses is 200 µs,
the displacement ∆xi (t) = xi (t + ∆t) − xi (t) of the object(i) is 2 µm during the time interval ∆T , which is muchless than the spatial resolution ∆xS = TS × c0 /2=750 µm
of Fig. 2 in the depth direction when the sampling period TS is 1 µs. As shown in this example, the resultant
estimate xbi (t) of the next object position in (5) is represented not by a discrete value but by the continuous value

By applying the above method to each of the multiple N
points in the heart wall, the instantaneous object positionsxi (t), and the velocity signals v(xi ; t) are obtained for i =1, 2, . . . , N as shown in Fig. 1(b). At the beginning of thisprocedure, the initial positions (depth) {xi (t0 )} of the N
points {i} at a time t0 are manually preset at even intervalsof ∆xS along the ultrasonic beam in the heart wall, where∆xS is the spatial resolution in the depth direction. We
employ the time t0 at 200 ms before the first R-wave during
the A/D conversion, regarding it as near the end-diastole.
Thus, the initial positions are given by:xi (t0 ) = x1 (t0 ) + ∆xS × (i − 1),(6)where i = 1, 2, . . . , N . For example, for the presetting of
the initial positions in the IVS with reference to the longitudinal M-mode image, x1 (t0 ) and xN (t0 ) correspond to
the position on the surface of the right ventricle (RV) andthe surface of the left ventricle (LV) of the IVS, respectively. For the setting in the LV posterior wall, x1 (t0 ) andxN (t0 ) correspond to the positions on the endocardium
and the epicardium in the wall, respectively.
Let us assume that the ultrasonic beam is perpendicular to the heart wall during one cardiac cycle as shownin Fig. 1(a) and that the velocity direction of each point
i in the heart wall is parallel to the direction of the ultrasonic beam. Thus, from the difference between the instantaneous object position xi (t) and the instantaneous
position xi+1 (t) of the sequentially set point, the thicknessof the local region between points (i) and (i + 1), which isdenoted by hi (t), is obtained by:hi (t) = xi+1 (t) − xi (t) > 0. [m](7)Since the depth axis of Fig. 1(b) is positive in the downward direction, the thickness hi (t) in (7) is always positive
as shown in Fig. 1(d).
On the other hand, from the difference between the velocity values v(xi ; t) and v(xi+1 ; t), the instantaneous speed∆t hi (t) of the local change in thickness is obtained by:∆t hi (t) = v(xi+1 ; t) − v(xi ; t). [m/s](8)

When the region between the ith and (i + 1)-th points
become thicker at a time t, ∆t hi (t) > 0, while for the casewhen the region become thinner, ∆t hi (t) < 0. However,∆t hi (t) depends on the distance between xi (t) and xi+1 (t).
Thus, by dividing ∆t hi (t) by the distance |xi+1 (t) − xi (t)|,the normalized speed of the local change in thickness which

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ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 44, no. 4, july 1997

occurs in the assumed homogeneous myocardium between
points (i) and (i + 1), denoted by Si (t), is defined by:
Si (t) =∆t hi (t). [(m/s)/m]|xi+1 (t) − xi (t)|(9)

In actual in vivo measurement for the IVS, for example,
the typical values of ∆t hi (t) and |xi+1 (t) − xi (t)| are 4
mm/s and 0.75 mm, respectively. For these values, Si (t)of (9) is 5.3 [(mm/s)/mm]. By multiplying an appropriate
short period δT0 and the thickness of the region by the numerator in the right-hand side of (9), the thickness change
which occurs in the region per period δT0 is estimated.
Thus, Si (t) of (9) yields a generalized form because Si (t)does not depend on the PRF nor on the spatial resolution∆xS directly determined by the sampling period TS in theA/D conversion.
The spatial distributions {Si (t)} of the normalized
speed of the local change in thickness are color coded andsuperimposed on the M-mode image. In this paper, redcorresponds to thinning of the myocardium (Si (t) < 0)and blue corresponds to thickening of the myocardium(Si (t) > 0) as shown in Fig. 6(1-d). The color scheme
corresponds to the temperature increase due to the adiabatic contraction and the temperature decrease due to theadiabatic expansion, respectively. This color scheme differsfrom that employed in standard color Doppler imaging [11]or tissue Doppler imaging [35]–[37] because the color coding in those systems is determined not by the speed ofthe local change in thickness but by the estimated local
instantaneous velocity.

IV. A System for Measurement and Analysis
In order to realize the procedure proposed in Sections II
and III, a high speed A/D converter with a large-scale
memory and an engineering workstation are employed
to analyze the analytic signal, y(t), resulting from thequadrature-modulation of the signal z(t) received by thesector-type ultrasonic transducer of the standard ultrasonic diagnostic equipment (Toshiba SSH-160A). In the diagnostic equipment, the standard B-mode cross-sectional
image and M-mode image are displayed to identify themeasurement points on the heart wall. The frequency
f0 of the transmitted ultrasound and repetition interval∆T =(1/PRF) of the transmission of the ultrasonic pulses
are set at 3 MHz and 222 µs, respectively, in the experiments in the following sections. At these conditions, theupper limit |vmax | of the velocity measurement, which is
free from the aliasing effect, is given by:|vmax | =c0
= 0.462 m/s,
4f0 ∆T(10)

when the acoustic speed c0 is assumed to be 1540 m/s.
The upper limit is much greater than the velocity of the
LV wall.
The signal, z(t), received by the ultrasonic transducer
is amplified and quadrature-demodulated by the ultra-

sonic diagnostic equipment. The resultant in-phase signal
and the quadrature signal are simultaneously A/D converted with a 2-channel 12-bit A/D converter at a sampling rate of 1/TS . The sampling rate 1/TS in the system
is variable from 1 MHz to 10 MHz; 1 MHz is employedin the following experiments. Thus, the spatial resolution∆xS = TS · c0 /2 in the depth direction is about 0.75 mm.
In the A/D converter employed, the length of each signal
is limited to 1,046,000 points (' 1 Mega words). However,these two signals are digitized only for the period of length
T0 where at least the signals reflected at the N points arereceived by the ultrasonic transducer. Thus, the effective
length of the digital signal in the A/D converter is increased from 1 second (= 1 Mega × TS ) to several seconds(= 1 Mega × TS × ∆T /T0 ), that is, several heartbeat periods because the typical values of ∆T and T0 are 222 µs and35 µs, respectively, for the experiments in this paper. For
this intermittent digitization, a sampling clock of 1 MHz is
generated only for the period T0 by an external signal generator, which is completely synchronous with the masterclock of the ultrasonic diagnostic equipment. The electrocardiogram (ECG) and phonocardiogram (PCG) are also
digitized so that their acquisition timing is synchronouswith that of the ultrasonic wave transmission from thetransducer. Then, the proposed method described in Sections II and III is applied to the resultant digital signals,
which are transferred from the A/D converter to the workstation via a GPIB interface. Each resultant velocity signal v(xi ; t) obtained by the proposed method is passed
through the digital low-pass filter with a cut-off frequency
fc of 600 Hz, which is realized by the finite impulse response (FIR) filter of the Hamming window with a lengthof 3.3 ms.

V. Experimental Evaluation of Measurable
Lower Limit Using Water Tank
In a previous paper [1], the principle of the method
proposed in Section II was confirmed using a water tankwhich simulated the small vibration of the ventricle wall on
the motion with large amplitude of ±7.5 mm caused by theheartbeat. Briefly, for large amplitude motion caused by
the eccentric cam in the water tank, the tracking result of
the surface of the rubber plate exactly coincided with the
M-mode image. For small vibration with a peak-to-peakamplitude of about 20 µm generated by a small vibrator on
the eccentric cam, evaluation using the squared-magnitudeof the coherence function showed that the small velocity
signal on the large motion was successfully detected in thefrequency range from 1 to 1000 Hz.
In this paper, in addition to the above experiments,
the lower limit of the measurable velocity and the thickness change is evaluated using a rubber plate fixed in awater tank. The longitudinal velocity c0 in the rubber isabout 1.5 × 103 m/s. The measurement system describedin Section IV is employed with the same values for theparameters of f0 , ∆T , TS , and fc .

kanai et al.: myocardial thickening and color-coded imaging

Fig. 3. Experimental results for evaluation of measurable lower limit
using a water tank. (a): The object motion xs (t) and xi (t) estimatedby the proposed method, superimposed on the M-mode image obtained by the magnitude of the received signal. (b) and (c): The
velocity signal estimates v(xs ; t) and v(xi ; t) of points (s) and (i).
(d): The change in thickness, h(t), between point (i) and (s) obtained
from v(xs ; t) and v(xi ; t).

Fig. 3(a) shows the M-mode image obtained from themagnitude of the received signal. The positions xs (t) andxi (t) of point (s) on the rubber surface and point (i) in therubber, respectively, are manually preset at the leftmost
timing in Fig. 3(a). The distance between these points is0.75 mm. The tracking results superimposed in Fig. 3(a)show that xs (t) and xi (t) are almost straight lines.
Figs. 3(b) and (c) show that the velocity signals v(xs ; t)and v(xi ; t) at points (s) and (i) obtained by the proposed
method. By integrating the difference between v(xs ; t) andv(xi ; t), the change in thickness, h(t), of (7) is obtained asshown in Fig. 3(d).
The vertical axis of Figs. 3(b)-(d) is magnified so thatthe noise component of each signal can be shown. Eachsignal should be zero if the signal-to-noise ratio is infinite.
From Figs. 3(b) and (d), the lower limit |vmin | of the velocity measurement is approximately given by:|vmin | = 0.1 mm/s,(11)which is less than 1/2000 of the upper limit |vmax | =462 mm/s of the measurable velocity in (10). Since |vmax |corresponds to π radian of the phase-shift during the pulse
repetition interval ∆T , error in the phase-shift detection isless than 0.04 degree (= 0.1 [mm/s] × 180◦ /462 [mm/s]).
The dynamic range of the velocity measurement is givenby:dynamic range = 20 log

vmax= 73 dB.
vmin

(12)

From Fig. 3(d), the lower limit |hmin | of the measurementof the change in thickness between these two points (s) and(i) in the developed measurement system is approximately
given by:|hmin | = 0.1 µm.

(13)

757

Fig. 4. A standard B-mode short-axis image showing the crosssectional area around the detected points preset in the interventricular (IVS) in an in vivo experiment for the detection of their instantaneous positions and the velocity signals of a presumedly healthy
26-year-old male volunteer. Points (R) and (L) are on the RV surface and the LV surface of the IVS, respectively. The ultrasonic beampassing through the two points is almost perpendicular to the septum
during the measurements.

From these experiments, sufficient accuracy and precision
have been confirmed.

VI. In Vivo Experimental Results for theInterventricular Septum
A. Explanation of the Procedure of the Proposed Method
The proposed method is applied to the detectionof velocity signals on the IVS of a healthy 26-yearold male volunteer. Fig. 4 shows the B-mode image of
the LV in the short axis, which was obtained by standard ultrasonic diagnostic equipment. The 14 points {i}are set in the region from point (R) on the RV surface to point (L) near the LV side of the IVS, wherexR (t) = x1 (t) and xL (t) = x14 (t). Since the results
obtained by the proposed method depend on the angle between the direction of the velocity vector and theultrasonic beam, the direction of the ultrasonic beampassing through points (R) and (L) is selected so thatthe beam is on the LV center in the cross-section
and is almost perpendicular to the IVS, as shown in
Fig. 4, during the A/D conversion of several cardiac cycles. During the acquisition period, respiration is suspended.
Figs. 5(a) and (b) show the ECG and PCG, respectively. Fig. 5(c) shows the M-mode image which was reconstructed from the magnitude of the digitized signalof the analytic signals. Before applying the method described in Section II, by referring to the M-mode image of
Fig. 5(c), the positions {bxi (t0 )} of the 14 points {i} aremanually preset using the workstation at even intervalsof ∆xS =0.75 mm from point (R) near the surface of theRV side of the IV to point (L) near the surface of the LV

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Fig. 5(f) shows the thickness change, {xbi (t) − x
c1 (t)},
that occurs in the region between the point (R) on surfaceof the RV side and the ith point in the IVS. Each waveformof {xbi (t)−cx1 (t)} is also almost completely reproducible forthe five heartbeat periods. For the systolic phase, the IVS
becomes about 3 mm thicker than that of the diastolic
phase, where the thickness of the IVS is about 10 mm at
the end of the diastole.
Fig. 5(g) shows the normalized speed of the local change
in thickness, {Si (t)}, of (9), which occurs in the local region between points {i} and {i + 1}. In this figure, theirabsolute values {|Si (t)|} are mapped as black and white
and the results are superimposed on the tracking results{bxi (t)} of Fig. 5(d). For the region and the timing where
there is a large change in thickness in Fig. 5(f), for example, for the beginning and the end of the systole especiallyat the LV side in the IVS, the instantaneous local change
in thickness is found to be large.
B. Color-Coded Imaging

Fig. 5. In vivo experimental results of instantaneous object positionand velocity estimated at 14 points {i} preset in the IVS of thenormal young male subject in Fig. 4. (a): ECG. (b): PCG. (c): The
M-mode image. (d): The tracking results {bxi (t)} in (7) of the 14
points {i}, which correspond to the illustration of Fig. 1(b). These
results are superimposed on the M-mode image in (c). The points (R)and (L) correspond to the surface on the RV side and the surface near
the LV side of the IVS, respectively. (e): Superimposed estimates ofthe velocity signals {bv (xi ; t)} of the 14 points {i} in the heart wall.
xi (t) − b
x1 (t)}, from the RV side to the(f): The change in thickness, {bith point in the IVS for i = 1, 2, . . . , 14. (g): The normalized speed ofthe local change in thickness, {Si (t)} [(m/s)/m], which occurs in theregion between points {i} and {i + 1}. The absolute values {|Si (t)|}are mapped using black and white and the results are superimposedon the tracking results of (d).

By magnifying the time axis in Fig. 5, Fig. 6(1)shows the results for the first cardiac cycle. Fig. 6(1d) shows the tracking results {bxi (t)} of the 14 points{i} by white lines and the normalized speed of thelocal change in thickness, {Si (t)}, of (9). The values{Si (t)} are color coded according to the coloring scheme
described in Section III and the results are superimposed on the M-mode image of Fig. 6(1-c). Fig. 6(1e) shows superimposed estimates of the velocity signals {bv (xi ; t)} of the 14 points {i} in the heart wall.
Especially for the period of the beginning of the systole and the beginning of the diastole after the second heart sound (II), there are relatively large differences between the velocity estimates, which correspond to the thickening and thinning, respectively, inthe heart wall. For the period around the R-wave andthe center of the diastole, however, these velocity estimates coincide with each other, which corresponds tothe parallel motion as illustrated in Fig. 1(c). Fig. 6(1f) shows the change in thickness, {bxi (t) − x
b1 (t)}, between the RV side and the ith point in the IVS for
i = 1, 2, . . . , 14.
C. Spectrum Analysis of the Velocity Signals

side. The tracking results {bxi (t)}, estimated by (5) of the
14 points {i}, are superimposed on the M-mode image asshown in Fig. 5(d).
Fig. 5(e) shows the superimposed estimates of the velocity signals {bv (xi ; t)} on the tracked points {xbi (t)},where i = 1, 2, . . . , 14. The vertical axis of Fig. 5(e) isinverted so that the negative value of the velocity, whichis shown above the baseline, corresponds to the situationin which the object moves in the direction of the ultrasonic transducer on the chest wall, which is more easily
understood. The resultant vibration signals are sufficiently
reproducible for five heartbeat periods.

Figs. {7(c-i)} (i=1, 3, 5, 7, 9, 11, 13) separately showeach of the velocity signals {bv (xi ; t)} for 7 of the 14 pointsof Fig. 5(e). In these figures, the results for the first 5
heartbeats are overlaid and shown. Around the center ofthe systolic phase, the velocity estimates {bv (xi ; t)} in the
IVS have small positive values for about 200 ms as shownin Fig. 7(c), which means that the IVS slowly moves tothe LV. The amplitude of vb(x1 ; t) of Fig. 7(c-13) on the
LV side is a little greater than that of vb(xR ; t) of Fig. 7(c1) on the RV side, especially in the systolic phase. Thisdifference corresponds to the change in thickness due tothe expansion in the wall of the IVS.

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Fig. 6. In vivo experimental results of the instantaneous object position and the velocity estimated at 14 points {i} in the IVS for the
first cardiac cycle. (1) the normal subject in Fig. 5. (2) a 32-yearold male patient with acute lymphoblastic leukemia and with serious
cardiomyopathy, who had been treated with antracenadiones, where
the measurement was performed five months before his death. (3)the same serious patient as Fig. 6(2), where the measurement was
performed two months before his death and three months after themeasurement in Fig. 6(2). (a): ECG. (b): PCG. (c): The M-mode
image. (d): The tracking results {bxi (t)} in (7) of the 14 points {i}are shown by white lines. The normalized speed of the change inthickness, Si (t) [(m/s)/m], is mapped according to the defined color
scheme and is superimposed on the tracking results. (e): Superimposed estimates of the velocity signals {bv (xi ; t)} of the 14 points {i}xi (t) − b
x1 (t), in thein the heart wall. (f): The change in thickness, b
region from the RV side to the ith point in the IVS for i = 1, 2, . . . , 14.

Figs. {7(d-i)} (i=1, 3, 5, 7, 9, 11, 13) show the average power spectra {P (xi ; f )} of {bv (xi ; t)} in Figs. {7(c-i)}.
Each spectrum is obtained by applying FFT to vb(xi ; t) forthe period of ±100 ms around the timing of the second
heart sound (II) in Fig. 7(a) for each heartbeat, where
the Hanning window is employed. The vertical bar foreach frequency shows the minimum and maximum values of the power spectra of the velocity signals in the first
five heartbeats. As shown in these figures, there are large
components in the low frequency range less than 25 Hz,
which correspond to the large motion due to the heartbeats. There is sufficient reproducibility even for the highfrequency components from 25 Hz to 90 Hz. The frequency
component at 90 Hz is less than the maximum component
at 10 Hz by about 20 dB. Even for these small components,

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which are within the thickness of the overlaid curves in
Figs. {7(c-i)}, the waveform is accurately detected by the
proposed method.
By applying the power spectra {P (xi ; f )} of the velocity signals {bv (xi ; t)} detected for the points from theRV surface to near the LV surface in the IVS, there are
increases of power from P (x1 ; f ) to P (x13 ; f ), which aresimilar to those in the velocity signals in Figs. {7(c-i)}
due to the thickening and thinning in the heart wall in the
period around the second heart sound (II). However, comparison of the power at each frequency in Figs. {7(d-i)}
shows that an increase of power occurs in the frequency
band from 25 Hz to about 90 Hz, while for the components
in the frequency band less than 25 Hz, there is little difference in power. From these results, the dominant frequency
band of the components generated by the thickening andthinning in the heart wall at the timing around the second
heart sound, which is shown by red and blue in Fig. 6(1-d),
is from 25 Hz to at least 90 Hz.
To quantitatively evaluate the reproducibility of thesimilarity of the M -heartbeat velocity signals {vbj (xi ; t)}(j = 1, 2, . . . , M ) for each frequency component of f ,where subscript j denotes the cardiac cycle number, thereproducibility function |γ0 (f )|2 was introduced in the previous report [1]. The range of |bγ0 (f )|2 is from 0 to 1. If
2|b
γ0 (f )| is equal to 1, the velocity signals {vbj (xi ; t)} in
the M heartbeats completely coincide for the frequency
component of f . If |bγ0 (f )|2 is zero, there is no correlation among {vbj (xi ; t)} for the frequency components of f .
Figs. {7(e-i)} (i=1, 3, 5, 7, 9, 11, 13) show the reproducibility function, |γ0 (f )|2 , of the velocity signals {bv (xi ; t)} forthe first 5 heartbeats in Figs. {7(c-i)}. The analyzed periods are the same as those in Figs. {7(d-i)}. In each result
from Fig. 7(e-1) to Fig. 7(e-13), there is a high correlation between these velocity signals for the 5 heartbeats up
to about 100 Hz. Thus, the reproducibility of the velocity
signals of each point in the myocardium is quantitatively
confirmed.
D. Spectrum Analysis of the Speed of Thickness Change
Figs. 8(c), (d), and (e) show the instantaneous speed∆t hi (t) = vb(xi+2 ; t) − vb(xi ; t) of the change in thicknessof (8) for the velocity signals in Fig. 5(f), the magnitude of transfer function H(xi → xi+2 ; f ) from v(xi ; t) tov(xi+2 ; t), and the squared-magnitude of coherence function γ(xi → xi+2 ; f ), respectively, estimated in 6 regionsin the IVS. These functions are defined in [1], [38]. In
Figs. {8(c-i)} (i=1, 3, 5, 7, 9, 11), the results for the first
5 heartbeats are overlaid and shown. The vertical axis ismagnified by 4 to those in Figs. {7(c-i)}. Fig. 8(c-0), bottom left, shows the instantaneous speed of the thickness
change vb(x14 ; t) − vb(x1 ; t) of the IVS. Especially in thesystole, there are large thickness changes.
In Figs. {8(d-i)} (i=1, 3, 5, 7, 9, 11), the period analyzed and the window employed are the same as those in
Fig. 7. As with the results in Fig. 7(d), for these transfer
functions also a large increase in power is found to occur

in the frequency band from 25 Hz to 90 Hz. Especially in
Fig. 7(d-0), the bottom figure, which shows the magnitudeof the transfer function from {bv (x1 ; t)} of the RV surface to{bv (x14 ; t)} near the LV surface of the IVS, the results areclearly recognized. The magnitude of the transfer function,
which corresponds to the amplitude increase of vb(x14 ; t) tovb(x1 ; t) due to the thickening of the myocardium, is about
5 dB in the frequency band from 25 Hz to 90 Hz.
In Figs. {8(e-i)} (i=1, 3, 5, 7, 9, 11), the analyzed periods are the same as those in Fig. 8(d). There is a highcorrelation between these small velocity signals for the first
5 heartbeats up to about 90 Hz.
VII. Regional Myocardial Layer Function in a
Patient with Acute Lymphoblastic Leukemia
As an example of noninvasive diagnosis of myocardialdamage induced by adriamycin injection, we applied the
proposed method to a patient with serious cardiomyopathy.
A. Velocity Signals, Change in Thickness,
and Color-Coded Imaging
For a 32-year-old male patient with acute lymphoblastic leukemia, who had been treated with antracenadiones (mitoxantrone) and who suffered from Doxorubicincardiotoxicity, the waveforms of the velocity signals, thickness change, and Si (t) in the IVS are shown in Figs. 6(2)and (3). The subject suffered from severe cardiomyopathy. Three months after the measurement in Fig. 6(2),the measurements were repeated for the same patient (inFig. 6)(3). About two months after the last measurement,
the subject died from the congestive heart failure.
As shown in Figs. 6(2) and (3), the results are quite
different from those of the normal subject represented inFig. 6(1). For the velocity signals in Figs. 6(2-e) and (3e), the amplitude of the signals, especially for the higher
frequency components, are smaller than that of the normal
subject. As can be seen from Figs. 6(2-f) and (3-f), there islittle change in thickness of the IVS. The maximum valuesof the change in thickness of the IVS are about 850 µm
in Fig. 6(2-f) and 490 µm in Fig. 6(3-f). For the normal
subject, however, the value is about 3600 µm as shown in
Fig. 6(1-f).
There are also clear differences in the spatial-time distributions of {Si (t)} in Figs. 6(2-d) and (3-d) from thosein Fig. 6(1-d). For the normal subject, thickening and/or
thinning occur simultaneously in time and homogeneously
across the LV wall. For the serious patient, however, theperiodic change in each layer thickening with the cardiac
cycle disappears and, moreover, the heterogeneous behavior across the LV wall becomes obvious.
B. Spectrum Analysis
Fig. 9 shows the velocity signals, their power spectra,
and the reproducibility function, estimated at 7 points in
the IVS for the same patient. The measurement was performed two months before his death, the same as that inkanai et al.: myocardial thickening and color-coded imaging

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Fig. 7. The velocity signals, their power spectra, and the reproducibility functions, estimated at 7 points in the IVS for the first 5 heartbeatsof the normal young male subject in Figs. 4, 5, and 6(1). (a): PCG. (b): ECG. (c-i): the detected velocity signal bv (xi ; t) (i=1, 3, 5, 7, 9, 11,13) at the 7 points from the RV surface to near the LV surface in the IVS. In Figs. (a), (b), and (c), the results for the first 5 heartbeats arev (xi ; t) in (c-i). The vertical bar for each frequency shows the minimum
overlaid and shown. (d-i): The average power spectrum P (xi ; f ) of b
and maximum values of the power spectra of the velocity signals in the heartbeats. (e-i): The reproducibility function, |γ0 (f )|2 , of thevelocity signals {bv (xi ; t)} for the heartbeats in Fig. (c-i). There is a high correlation between these signals for the heartbeats up to about
100 Hz.

Fig. 6(3). By comparing the velocity signals and the power
spectra in Figs. 9(c) and (d) with those of the normal subject in Figs. 7(c) and (d), it can be seen that the signal
power is greatly decreased, especially for the frequency
components higher than 50 Hz. In this frequency band,as described above for the results in Figs. {7(c-i)} for thenormal subject, there are large differences of the velocity
signals between both sides of the IVS, and these differences generate the thickening and thinning components in
the heart wall. For the serious patient, however, the factthat the thickness change of the IVS is not recognized at
all corresponds to the lack of the frequency component inthis frequency band.
Fig. 10 shows the instantaneous speed ∆t hi (t) of the
thickness change of (8), the transfer function H(xi →xi+1 ; f ) from v(xi ; t) to v(xi+2 ; t), and the squared-

magnitude of coherence function, estimated in 6 regionsin the IVS for the patient represented in Fig. 6(3). The
amplitude of the instantaneous speed ∆t hi (t) of the thickness change for all local regions in the IVS other than theregion between the 7th point and 9th point in Fig. 10(c-7)
is very small as shown in Fig. 10(c). Regarding the magnitude of the transfer function in Fig. 10(d), the values arealmost 0 dB; this means that the components due to thethickening and thinning cannot be recognized.
These differences between the normal subject and theserious patient correspond to the changes in the acousticalcharacteristics of the local heart wall due to the injectionof mitoxantrone. Mitoxantrone has been reported to havean adverse cardiotoxic effect, which results in irreversible
diffuse myocardial fibrosis at cumulative or high doses[39]. Taking these experimental results into account, the762

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Fig. 8. The instantaneous speed of the thickness change, the transfer function, and the coherence function, estimated in 6 local regions in
the IVS for the 5 heartbeats of the normal young male subject in Figs. 4, 5, 6(1), and 7. (a): PCG. (b): ECG. (c-i): The instantaneous speed∆t hi (t) of the change in thickness, where i=1, 3, 5, 7, 9, 11 in 6 regions preset from the RV surface to the LV surface in the IVS. In (a),(b), and (c), the results for the first 5 heartbeat are overlaid and shown. (d-i): The magnitude of the transfer function H(xi → xi+2 ; f )from bv (xi ; t) to bv (xi+2 ; t) in (c). (e-i): The squared-magnitude of the coherence function, |γi,i+2 (f )|2 , between signals bv (xi ; t) and bv (xi+2 ; t)in (c). (c-0), (d-0), and (e-0): The respective results for the data between bv (xR ; t) = bv (x1 ; t) on the RV surface and bv (x14 ; t) near the LV
surface in the IVS.

method proposed in this paper provides a new approachto the detection of such myocardial physical and/or histological heterogeneity by analyzing velocity waveform andthe instantaneous local change in thickness of the heart
wall detected noninvasively from the chest surface.
VIII. In Vivo Experimental Results for LV
Posterior Wall
Figs. 11(1) and (2) show the experimental results obtained by applying the proposed method to the LV posterior wall of another 22-year-old male subject and thepatient with serious cardiomyopathy in Fig. 6(3), respectively. The latter measurement was performed two months
before the patient’s death. The 19 points are set at evenintervals of ∆xS = 0.75 mm from the endocardium of the

LV posterior wall to the epicardium as shown in Figs. 11(1d) and (2-d). The ultrasonic beam passing through thesepoints is almost perpendicular to the posterior wall during the measurements. The display format in Figs. 11(1)and (2) is similar to that in Figs. 6(1), (2), and (3).
In Figs. 11(1) and (2), however, the maximum value ofthe vertical axis is 0.15 m/s and the maximum valueof 5 [(m/s)/m] of the normalized speed of the thickness
change is replaced by 10 [(m/s)/m], since the amplitude of
the motion is larger in the posterior free wall. The waveforms of the velocity signals are seen to be quite different
from those in the IVS.
From Figs. 11(1-c), (2-c), (1-d), and (2-d), it can beseen that there is parallel motion due to the heartbeatwith an amplitude of about 8.6 mm for the normal subject
and about 4.5 mm for the patient. For the normal subject

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Fig. 9. The velocity signals, their power spectra, and the reproducibility function, estimated at 7 points in the IVS for the 8 heartbeats ofthe serious patient in Fig. 6(3). The measurement was performed two months before his death. (For details see Fig. 6.)

represented in Fig. 11(1-f), the thickness of the posteriorwall is about 12 mm at the end of the diastole and thewall becomes about 6 mm thicker for the systolic phasethan that of the diastolic phase. For the serious patient in
Fig. 11(2-f), however, the wall becomes only about 3 mm
thicker in the systolic phase than in the diastolic phase.
At the same time, the normalized speed of the thickness
change during the myocardial relaxation for the diastole,
which is the gradient of the lines in Fig. 11(1-f), is different
from that in Fig. 11(2-f).
IX. Discussion
A. Measurement of Velocity and Displacement
All the techniques for velocity estimation employedin pulse-Doppler systems rely on the relationship of (1)between the phase-shift ∆θ(xi ; t) and the displacement∆xi (t) during the interval ∆T of consecutive echoes. To

determine the phase-shift ∆θ(xi ; t), an efficient complex
cross-correlation technique has been developed in [11] forreal-time two-dimensional blood flow imaging. Since thecross-correlation is averaged over a duration of about 10
received echoes in the actual system, the time resolutionof the resultant waveform is not so high.
The theoretical limitations of the phase-shift measurement are explained in [34] as follows: Variance of the estimation of the phase-shift increases if broadband excitation is employed to improve the range-resolution; andthe propagation-attenuation effect introduces the bias error due to the shift of the center frequency in the received
echoes. These limitations are also not overcome in our
method.
To improve the range-resolution and accuracy of theestimated velocity and overcome the velocity-limitationof the pulse Doppler due to the aliasing effect, the velocity and the displacement are directly estimated bytime-shift measurement using the local cross-correlation

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Fig. 10. The instantaneous speed ∆t hi (t) of the thickness change of (10), the transfer function H(xi → xi+2 ; f ) from v(xi ; t) to v(xi+2 ; t),and the coherence function, estimated in 6 regions in the IVS for the 8 heartbeats of the serious patient in Figs. 6(3) and 9. The measurement
was performed two months before his death. (For details see Fig. 8.)

between consecutive RF signals in [34]. When the velocity and/or displacement are determined by the crosscorrelation function of the RF signal, measurement of displacement of 2 µm would require a very high frequency of
375 MHz ( = 1500 [m/s]/(2 [µm] × 2)). To improve the estimation precision in the cross-correlation function of subsampled RF signals, several interpolation methods havebeen proposed and their performances are compared in[33]. Reconstruction interpolation, although entailing highcomputational costs, can decrease bias error in the timedelay estimation to subnanoseconds, which corresponds tothe displacement of submicrometers. However, a high sampling frequency of about 50 MHz is still required by thisinterpolation method.
As confirmed by the experiment in Section V, the lowest
measurable velocity by our method is about 0.1 mm/s,
and the lowest measurable change in thickness and thedisplacement is about 0.1 µm.

B. Comparison of Color-Coded Imaging Between the
Proposed Method and Tissue Doppler Imaging
For the display of the local velocity in the myocardium,tissue Doppler imaging has been already developed [35]–[37]. By this method, the color code determined from thelocal instantaneous velocity is superimposed on both Mmode and B-mode images. The lowest measurable velocity of the system based on the conventional color Doppler
imaging technique is 2 mm/s [37]. Using the same data
set of the IVS and the posterior wall of a 23-year-old malewith Doxorubicin-cardiotoxicity at complete remission, thenormalized speed of the change in thickness obtained by
the proposed method and the superimposed M-mode image obtained by the tissue Doppler method are comparedin Figs. 12(1) and (2), respectively.
In the results obtained by tissue Doppler imaging shownin Fig. 12(2), the color code of each point in the heart wall

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Fig. 11. In vivo experimental results of the instantaneous object position and the velocity estimated at 19 points {i} in the posterior wallof another normal subject (1) and the same serious patient (2) as Fig. 6(3), where the measurement was performed two months beforechis death.. (a): ECG. (b): PCG. (c): The M-mode image. Two white lines show the estimated instantaneous positions xb1 (t) = x
R (t) andxccxi (t)} in (7) of the 19 points {i} are shown
19 (t) = x
L (t) on the endocardium and the epicardium, respectively. (d): The tracking results {bby white lines. The normalized speed of the change in thickness, Si (t) [(m/s)/m], is mapped according to the defined color scheme and issuperimposed on the tracking results. (e): Superimposed estimates of the velocity signals {bv (xi ; t)} of the 19 points {i} in the heart wall.
xi (t) − b
x1 (t), in the region from the endocardium to the ith point in the posterior wall for i = 1, 2, . . . , 19.
(f): The change in thickness, b

is determined by the velocity and its polarity. Namely, it
is determined by the sum of the parallel global motion andthe local change in thickness. However, since the amplitudeof the parallel global motion is dominant, the spatial distribution of the velocity in the IVS and the posterior wall
is not so clear, that is, the image reflects the global motionof the LV wall relative to the precordial probe, but not the
myocardial layer thickening/thinning across the LV wall.

For the normalized speed of the change in thickness
obtained by the proposed method, however, the parallel
global motion with large amplitude induced by the cardiac beat is canceled and, consequently, the color code on
the M-mode image discriminates the instantaneous change
in thickness in the local area around each point as shown in
Fig. 12(1). The noninvasive evaluation of spatial distribution of speed of local myocardial thickening/thinning has
not been realized in the conventional ultrasonic diagnosis
systems, and the proposed method has the potential toprovide information relative to the noninvasive diagnosisof myocardial local motility.

C. Advantages of the Proposed Method
for Spectrum Analysis

The velocity signal measurement by the proposed
method has the following advantages compared with theconventional methods.
1. The measurable frequency band is from d.c. to several hundred Hz. Since components in the frequency band
higher than 100 Hz in the velocity signal of the heart wall
are not large, the velocity signals of the frequency band, atleast until 100 Hz, are accurately measured with sufficient
reproducibility.
2. With standard Doppler equipment and in almost all
the methods, including the wall-tracking techniques reported in the literature, the measured velocity and/or the
displacement are displayed in the time domain. The effective frequency band is less than 20 Hz and the frequency
components from 20 Hz to 100 Hz are not considered. As
shown in Fig. 8(d-0), however, the dominant componentof the change in thickness is in this frequency band. Thus,
for the accurate detection of the change in thickness of the766

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Fig. 12. In vivo experimental results obtained by the proposed method (1) and the tissue Doppler imaging (2) at multiple points {i} in the
IVS and the posterior wall of a 23-year-old male patient with mild cardiomyopathy. The tracking results {bxi (t)} in (7) of the multiple points{i} are shown by white lines. (1): The normalized speed of the change in thickness, Si (t) [(m/s)/m], is mapped according to the definedcolor scheme and is superimposed on the tracking results. (2): The velocity, v(xi ; t) [(m/s)], is mapped according to the defined color scheme
and is superimposed on the tracking results.

myocardium, it is essential to measure such high frequency
components; our method is the first to achieve this.
3. As evaluated in Section V, the proposed method has
a wide dynamic range of about 73 dB, the spectrum analysis being applied even for frequency band higher than
20 Hz to 100 Hz, where the amplitude of the frequency
components is very small, i.e., several micrometers. Thesehigh frequency components with small amplitude are also
accurately measured by our method with sufficient reproducibility.
X. Conclusions
In this paper we have proposed a new noninvasive
method for evaluation of local thickness change in theheart wall using ultrasound. By an in vivo measurement
system to realize this method, both the instantaneous positions and the velocity signals of the multiple points preset in the heart wall are accurately detected in the frequency range up to 100 Hz with sufficient reproducibility.
By color-coded imaging, moreover, the spatial-time distribution of the instantaneous local change in thickness of theheart wall are obtained. For a serious patient, the results
are quite different from those of the normal subject. From
the difference in the power spectra of the velocity signals
at multiple points in the heart wall, the frequency band

where the myocardial expansion and contraction occur is
identified. From the spectrum analysis of the velocity signal of the serious patient, the components in this frequency
band are greatly decreased.
Since these preliminary studies in this paper were performed in young patients with clear echocardiograms,
much work must be done to find out how the method canbe applied in a wider range of subjects and to see whether
it can contribute to assessment of myocardial diseases andrecovery. Further investigation of this proposed method,
including its clinical application to the noninvasive local
diagnosis of coronary artery disease, drug-induced myocardial disease, and arteriosclerosis of patients including elder
subjects, is being conducted. It will be necessary to compare the in vivo results obtained herein by the proposed
method with pathological findings in order to evaluate therange of variability in clinical studies and construct a standard which can be applied to the in vivo diagnosis of theheart wall.
The direction of the ultrasonic beam was selected sothat the beam was perpendicular to the heart wall in thispaper. It is necessary to overcome the limitation. It will
also be necessary to identify the origin of the parallel global
motion detected in this paper. In this study, detected velocity signals were analyzed in the frequency domain only
for the period around the second heart sound emission. Itkanai et al.: myocardial thickening and color-coded imaging

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will also be necessary to analyze the velocity signals forother periods, including systole and the end of diastole.

[17] W. T. Kemmerer, R. W. Ware, H. F. Stegall, J. L. Morgan, andR. Kirby, “Blood pressure measurement by Doppler ultrasonicdetection of arterial wall motion,” Surg. Gynec. Obstet., vol. 131,
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[18] K. Lindström, K. Marsal, G. Gennser, L. Bengtsson, M. Benthin, and P. Dahl, “Device for measurement of fetal breathing
movements. 1. The TD-recorder. A new system for recording the
distance between two echogenerating structures as a function oftime,” Ultrasound Med. Biol., vol. 3, pp. 143–151, 1977.
[19] D. E. Hokanson, D. E. Strandness, Jr., and C. W. Miller, “An
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Acknowledgments
The authors are grateful to Prof. Floyd Dunn of the
Bioacoustics Research Laboratory, the University of Illinois, and Prof. Kunio of Shirato of Tohoku University
School of Medicine for discussions and encouragement andto Associate Prof. Yoshiko Saito, Prof. Fumiaki Tezuka,
and Dr. Eiichi Kamata of Tohoku University School of
Medicine for helpful discussion and assistance with experiments. The authors also acknowledge the contributions ofMichie Sato, Kohshiro Sugimura, and Shigemitsu Nakaya
in our laboratory.
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Hiroshi Kanai (A’88–M’91) 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 at the Department of Electrical Engineering, Faculty of Engineering, Tohoku University. Since 1992 he has been an Associate
Professor at the Department of Electrical Engineering, Faculty ofEngineering, Tohoku University. His present interest is in ultrasonicmeasurements and digital signal processing for diagnosis of the heartdiseases and arteriosclerosis.
Dr. Kanai is a member of the Acoustical Society of Japan, the Institute of Electronics Information and Communication Engineeringof Japan, the Japan Society of Mechanical Engineers, the Japan Society of Ultrasonics in Medicine, Japan Society of Medical Electronics
and Biological Engineering, the Institute of Electrical Engineers ofJapan, the Japanese Circulation Society, and the Japanese College
of Cardiology.

Hideyuki Hasegawa was born in Tochigi,
Japan, on August 28, 1973. He received a B.E.
degree in electrical engineering from Tohoku
University, Sendai, Japan, in 1996.
Since 1996, he has been a postgraduate
student of the Department of Electrical andCommunication Engineering, Tohoku University, Japan. His current interest is in digital
signal processing and ultrasonic measurement
for cardiovascular disease and atherosclerosis.
Mr. Hasegawa is a member of the Acoustical Society of Japan, and the Institute ofElectrical Engineers of Japan.

Noriyoshi Chubachi (M’83) received B.S.,
M.S., and Ph.D. degrees in electrical engineering from Tohoku University, Sendai, Japan, in
1956, 1962, and 1965, respectively.
In 1965, he joined the Research Instituteof Electrical Communication, Tohoku University, where he was an associate professor from1966 to 1978. Since 1979 he has been a professor at the Department of Electrical Engineering, Tohoku University. From 1982 to 1983
he was a visiting Professor of Electrical andComputer Engineering, University of California, Santa Barbara, CA. He has worked on ultrasonic transducers anddelay lines, surface acoustic devices, acoustoelectronics, piezoelectricmaterials, acoustic microscopy, and related problems.

Dr. Chubachi is a member of the Acoustical Society of America, the Institute of Electronics and Communication Engineers ofJapan, the Society of Japanese Applied Physics, the Acoustical Society of Japan, the Japan Society of Ultrasonics in Medicine, theJapan Society for Nondestructive Inspection, the Japan Society of
Medical Electronics and Biological Engineering, the Japan Societyof Mechanical Engineers, and the Institute of Electrical Engineers ofJapan. He served as chairman of the Tokyo Chapter of IEEE UFFC
Society from 1987 to 1988. He is currently serving as Vice-Presidentof the Acoustical Society of Japan.

Yoshiro Koiwa was born in Sendai, Japan,
in 1944. He graduated from Tohoku University, Sendai, Japan, in 1969. He received his
M.D. degree from Tohoku University in 1977.
He is presently Associate Professor of First
Department of Internal Medicine of Tohoku
University. His main research interest is cardiovascular disease, especially cardiac function and heart failure.
Dr. Koiwa is member of American Federation for Clinical Research, the Japanese Circulation Society, the Japan Society of Ultrasonics in Medicine, and the Japan Society of Medical Electronics andBiological Engineering.

Motonao Tanaka was born in Japan in
1932. He received M.D. and the Ph.D. degrees in medical science from Tohoku University, Sendai, Japan, in 1959 and 1963, respectively. He was with the Research Institute for Chest Diseases and Cancer, Tohoku
University from 1959 to 1993 and with theInstitute of Development, Aging and Cancerfrom 1993 to 1994, where he was a Professor of Medicine and head of the Departmentof Medical Engineering and Cardiology. Since
1994 Dr. Tanaka has been the President of Tohoku Welfare Pension Hospital. His research interests are ultrasonics
in medicine and cardiology, especially cardiac function and tissue
characterization.
Dr. Tanaka is a member of World Federation for Ultrasound in
Medicine and Biology, the Japanese College of Cardiology, the Japan
Society of Ultrasonics in Medicine, the Acoustical Society of Japan,
and the Japan Society of Medical Electronics and Biological Engineering.