Ultrasound in Med. & Biol., Vol. 27, No. 4, pp. 481– 498, 2001
Copyright © 2001 World Federation for Ultrasound in Medicine & Biology
Printed in the USA. All rights reserved
0301-5629/01/$–see front matter

PII: S0301-5629(01)00341-6● Original Contribution
MYOCARDIAL RAPID VELOCITY DISTRIBUTIONHIROSHI KANAI* and YOSHIRO KOIWA†*Department of Electronic Engineering, Graduate School of Engineering; and †First Department of Internal
Medicine, Graduate School of Medicine, Tohoku University, Sendai, Japan(Received 9 June 2000; in final form 18 January 2001)

Abstract—Myocardial motion exhibits frequency components of up to 100 Hz, as found by a phased tracking
method. To simultaneously measure the rapid and minute velocity signals at multiple points along the surface ofthe left ventricle (LV), in this study, conventional ultrasonic diagnosis equipment was modified to allow 10 scanlines from a sector scanner to be arbitrarily selected in real-time for analysis. By considering the maximum valueof the velocity in the heart wall and the maximum depth from the chest surface, the number of transmission
directions of the ultrasonic pulses should be carefully confirmed to be 10 to avoid aliasing, which is much less than
the number employed in conventional tissue Doppler imaging (TDI). By applying the system, the velocity signals
at about 240 points in the heart walls were simultaneously measured for three healthy volunteers. During a shortperiod of 35 ms around end-diastole, the velocity signals varied spatially in the heart wall. At the end of systole,
in the wavelets near the base of the interventricular septum (IVS), the slow pulse continued for about 30 ms, justbefore the radiation timing of the second heart sound. Then, a steep pulse occurred just at the timing of theclosure of the aortic valve. The steep pulse at the base preceded that at the apex by several ms. By Fouriertransforming each wavelet, the spatial distribution of the phase of the steep pulse components were clearly
displayed. By applying the measurement method to two patients with aortic stenosis (AS), irregular vibration
signals, which correspond to the murmur of the heart sound, could be directly detected during the ejection
period. In conventional TDI, only the large slow movements due to the heartbeat are displayed, but these rapid
and minute velocity components cannot be displayed. In this study, moreover, the phase components weredetected for the first time from each of the velocity signals simultaneously measured at multiple points along the
10 scan lines. This measurement and method of analysis offer potential for new diagnostic techniques in cardiac
dysfunction. (E-mail: hkanai@ecei.tohoku.ac.jp) © 2001 World Federation for Ultrasound in Medicine &Biology.
Key Words: Heart wall tracking, Heart wall vibration, Myocardial motion, Rapid and minute velocity, Spatial
distribution, Left-ventricular end-diastolic pressure, Eigenvibration, Tissue Doppler imaging, Fourier analysis,
In vivo experiments.

INTRODUCTION AND LITERATURE

from 25 to 90 Hz contribute to regional myocardial thickening and thinning (Kanai et al. 1997). The rapid motion
measured in this study should be distinguished from theslow motion displayed in the M-mode or B-mode images
with large amplitude on the order of several hundred ␮mand with low frequency of less than 15 Hz.
Because tracking of the instantaneous position of
the heart wall is indispensable in the above measurement,
the correlation techniques previously devised for themeasurement of blood flow (Dotti et al. 1976; Bassini etal. 1982; Bonnefous and Pesque 1986; Suorsa et al.
1990; Jensen 1991; Hein et al. 1993; Hein and O’Brien
1993) and small slow motion of tissue (Adler et al. 1990;
Dickinson and Hill 1982; Tristam et al. 1988; de Jong etal. 1990; Hein et al. 1992) cannot be applied directly inthe measurement.

Measurement of rapid motion in the heart wall has novel
potential for use in diagnosis of regional myocardial
motility and viability. In this paper, the measured “rapid
motion” includes components with minute amplitude on
the order of several tens of ␮m up to several hundred Hz,
which has not been recognized in standard M-mode
echocardiography, B-mode echocardiography, nor in
TDI. It has already been experimentally shown that theFourier spectra of the rapid motion up to 100 Hz has
novel potential for use in diagnosis of myocardial fibrosis (Kanai et al. 1996) and that the frequency components
Address correspondence to: Hiroshi Kanai, Department of Electronic Engineering, Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan. E-mail: hkanai@ecei.tohoku.ac.jp
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The locations of the endocardium and epicardium
are traced by analyzing the M-mode image (Fleming etal. 1994), but only large slow motion of the wall isfollowed. The specular reflectors in M-mode images aretracked from the cross-correlation along digitized Mmode lines (Adler et al. 1990). However, the spatial
resolution is limited to several wavelengths, namely,
those more than 1 mm.
In the estimation of two-dimensional (2-D) strain
distribution or tissue elasticity (Ophir et al. 1991), thestrain is estimated by correlation between the radiofrequency (RF) echo pair acquired at precompression andpostcompression, but the minute strain that sequentiallyoccurs during the compression process, is not considered.
In sonoelasticity imaging, using color Doppler instruments (Lerner et al. 1990; Parker et al. 1990) or thecorrelation technique (Yamakoshi et al. 1990; Catheline
et al. 1999), 2-D spatial distribution of the amplitude andthe phase of the actuated minute rapid motion in soft
tissue or organs is displayed. The tracking operation,
however, has not been applied.
In TDI, the previous 2-D color-flow mapping instruments have been modified to acquire low-frequency
large-amplitude Doppler signals (Sutherland et al. 1994;
Yamazaki et al. 1996). The translation velocity and rotation velocity in the LV short-axis view have beenobtained (Watanabe et al. 1997) and the strain rate of theregional myocardium has been estimated (Heimdal et al.
1998). The velocity gradient, which assesses the regional
myocardial contractility, is also shown (Fleming et al.
1994; Uematsu et al. 1995). Various reports have validated TDI clinically (Miyatake et al. 1995; Donovan etal. 1995). However, only large slow motion due to theheartbeat is displayed in TDI. At the same time, thevelocity waveform in the heart wall is displayed at a low
sampling frequency of about 30 – 40 Hz (Fleming et al.
1994; Yamazaki et al. 1996). The clinical meanings ofthe velocity waveform and the velocity gradients havebeen investigated (Palka et al. 1995, 1996; Goecsan et al.
1996). However, because the sampling frequency is not
sufficiently high, the rapid and minute velocity components are not included in any of these results.
A digital echo-tracking method has also been applied to measure arterial wall motion, in which the zerocrossing point of the echo signal is tracked using a
flip-flop– based device (Hokanson et al. 1970), the elaborate phase-locked loop technique (Hokanson et al.
1972; Sainz et al. 1976; Korba et al. 1979; Rapoport andCousin 1982; Groves et al. 1982), or a high-speed A/Dconversion system of 25 MHz (Hoeks et al. 1990). The
spatial resolution in measurement of displacement is on
the order of tens of mm. A digital wall-tracking systemusing counting clock pulses of 27 MHz has also been

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proposed (Powalowski 1988). In these echo trackers,
however, only the phase of the received RF signal isconsidered. Furthermore, it is easily affected by additivenoise, as pointed out by Hartley et al. (1991), and it isdifficult to lock onto and remain locked to the desiredecho in in vivo experiments. As described in Kanai et al.
(1996), to track the rapid and minute motion in the heartwall, the quantization error in the determination of thezero-crossing point or the rising edge is still large (several ␮m), even when the sampling clock frequency, f CLK,
is 100 MHz.
We have already developed a novel ultrasonicbased method, namely, the phased tracking method, tomeasure the rapid velocity in the heart wall by accurately
tracking the movement x i (t) of a point (i) in the heart
wall by the constraint least squares method applied toboth the phase and magnitude of the quadrature-demodulated signals (Kanai et al. 1996). RF pulses are transmitted from an ultrasonic transducer at a pulse repetitioninterval ⌬T, and the reflected ultrasonic wave is received
by the same transducer and is multiplied by the original
RF signal in quadrature demodulation. By synchronizing
the pulse transmission timing and the acquisition timing
in A/D conversion rigidly with the original RF signal, theachieved lower limit 兩␷min兩 in the above velocity measurement is 0.1 mm/s, which was confirmed in phantom
experiments (Kanai et al. 1997), using the developed
method and system (Kanai et al. 1996). The lower limit
depends on the small dispersion in the above synchronization and on the additive noise in the received signal.
Because the lower limit 兩␷min兩 is less than 1/2000 of theupper limit 兩␷max兩 of the measurable velocity, which is
free from aliasing, the dynamic range of the velocity
measurement is given by 20 log10兩␷max兩/兩␷min兩 ⫽ 73 dB.
In phantom experiments (Kanai et al. 1996), a vibration
with small amplitude of 20 ␮m generated on the large
motion with an amplitude of ⫾7.5 mm and a frequencyof 1 Hz, which simulates heartbeat, was successfullymeasured in the range from 1 Hz to 1 kHz.
Application of the quadrature demodulation shifts
the spectrum peak from around the frequency ( f 0 ) of RF
US to around d.c. in the frequency domain. So long as
the employed acquisition frequency ( f s ) in the A/D
conversion is higher than the bandwidth of the original
spectrum around f 0 , no information is lost by the quadrature demodulation. For this measurement method, therefore, there are two kinds of spatial resolution along an
ultrasonic beam; one is the minimum spatial interval
between the succeeding points presettable in the heartwall, which is determined by the original frequency andbandwidth and is about 500 ␮m in the system. The otheris the lowest measurable displacement or change inthickness between two points, which is dependent on
precision in the above synchronization and additive noise

Myocardial velocity distribution ● H. KANAI and Y. KOIWA

483

Fig. 2. Three phases of a mode-2 vibration of an elastic spherical shell.

Fig. 1. Velocity signals on IVS measured by the phased tracking method for a healthy young subject. Five heartbeats areoverlaid. The discriminative pulsive waves at end-diastole andend-systole are indicated by ovals.

and is about 0.5 ␮m in the system, confirmed in separate
phantom experiments (Kanai et al. 1999c).
By applying this method and system to in vivo
experiments, the velocity signal, ␷ (t; x i ), of point i at a
depth of x i in the heart wall with small amplitudes, which
are less than several ␮m on the large motion resulting
from a heartbeat, can be successfully detected with reproducibility as shown in Fig. 1c and d. By applying
frequency analysis to the resultant velocity signal, ␷ (t;x i ), of the heart wall, the Fourier spectrum of ␷ (t; x i ) has
been obtained for the first time with sufficient reproducibility in the frequency range up to 100 Hz (Kanai et al.
1996). The developed method has already been realized
in a real-time measurement system (Kanai et al. 1999a).
Moreover, from the difference of the resultant velocity
signals { ␷ (t; x i )} between point x i and its succeeding
point x i⫹1 preset along the ultrasonic beam, a minutechange in thickness of several tens of ␮m has been
detected with spatial resolution of 0.5 ␮m (Kanai et al.
1999c), as described above. In this method, however,measurement of the velocity signal and the change inthickness is limited to multiple points along one scan lineof an ultrasonic beam passing through the object region.
To increase precision in the diagnosis, it is necessary to display the spatial distribution of these factors
without decreasing the temporal resolution and spatial
resolution along the depth axis. In this paper, by employing multiple 1-D configurations, each of which shows theaxial component along the ultrasonic beam with fastacquisition intervals, the 2-D spatial distribution of therapid velocity components is obtained on the cross-sectional 2-D image.
The proposed method is applied to the following
three fields in this paper.
1. Identification of mode-2 eigenvibration at end-diastole. LV pressure and its elasticity are significant
parameters necessary for the clinical diagnosis ofheart diseases. In particular, the LV end-diastolicpressure (LV-EDP), P ED , is usually needed to assess
the LV function in clinical settings. However, the
LV-EDP, the normal value of which lies between 5
and 12 mmHg, cannot be obtained from the bloodpressure measured at the brachial artery. Furthermore,
the LV end-diastolic elasticity (LV-EDE), E ED , cannot be noninvasively measured, and invasive catheterization is essential for the measurement of LV
pressure of a patient. Though this measurement has
high precision, such cardiac catheterization is difficult
to apply at the bedside. Therefore, a noninvasive
technique for measurement of LV-EDP (P ED ) and its
elasticity, E ED , is desired and has been developed asfollows:
By approximating the LV wall vibration at enddiastole by a free vibration of an elastic shell, as
shown in Fig. 2, Honda et al. (1994) have experimentally derived a simple relationship among the average
Young’s modulus E of the LV wall, LV internal
radius r, LV wall thickness h, myocardial density ␳,and LV instantaneous eigenfrequency f 2 of themode-2 eigenvibration. From experiments (Honda etal. 1994), it has been confirmed that the elasticity, E,of the shell is estimated from the two size parameters(r and h) and the mode-2 eigenfrequency f 2 without
measuring LV-EDP.
By theoretical analysis (Mirsky et al. 1974), furthermore, the LV elastic stiffness, E q , is given by thetwo size parameters (r and h) and the LV-EDP(P ED ). By assuming coincidence of the values ofthese two kinds of elasticity, E and E q , which havebeen differently derived, the LV-EDP (P ED ) is determined from the eigenfrequency f 2 of the LV wall
vibration and the two size parameters (r and h),which are measured by B-mode echocardiography.

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In in vivo experiments, the vibration ␷ (t) on the LVside of the IVS is measured by the phased tracking
method. By applying the short-time Fourier transformto ␷ (t), the instantaneous mode-2 eigenfrequency f 2 isdetermined at end-diastole. Using the f 2 , the LV-EDE(E ED ) and then the LV-EDP (P ED ) are determined.
The procedure has already been applied to five paˆ , have atients (Kanai et al. 1999b). The estimates, EEDsignificant correlation with the ratio, P ED /V ED[mmHg/mL], which has been employed for evaluation of the cardiac function, where the LV-EDP(P ED ) is directly measured by catheterization and the
LV end-diastolic volume V ED is measured by angiocardiography. Furthermore, the resultant pressure esˆ , almost coincides with the actual one,
timate, P

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is clarified, it will offer potential for novel quantitative assessment of myocardial viability.
3. Irregular vibration during ejection period in AS. For
patients with AS, a murmur, which is generated due tothe irregular blood flow around the aortic valve, isgenerally detected during the ejection period in theheart sound. For such patients, on the other hand, if
irregular vibrations are also directly detected in theheart wall by the phased tracking method, it will offer
novel information regarding the origin of the murmur
and the negative effect of the irregular blood flow on
the myocardium.
For the above three applications, the following procedures are employed in this paper. From in vivo experiments, novel results were obtained.

ED

P ED , invasively measured by a catheter in the LV.
Though the mode-2 eigenvibration of the LV has
been observed only in in vitro experiments with isolated canine hearts (Koiwa et al. 1988; Honda et al.
1994; Sato et al. 1996), it has not yet been confirmed
in in vivo experiments with human hearts. Therefore,
we applied the method developed in this study to the
LV wall of four subjects to confirm that there ismode-2 vibration on the LV wall at end-diastole
based on the spatial distribution of the frequency
component around 30 Hz in the resultant vibrations{ ␷ (t; x kj )}. For this purpose, it is necessary to simultaneously measure the rapid velocity signals at points
along each of multiple scan lines and to apply frequency analysis to each waveform.
2. Spatial delay-time detection of pulsive wave at endsystole. With the phased tracking method, it is possible to accurately detect small amplitude velocity signals of less than a few ␮m in the heart wall (Kanai etal. 1996). As shown in Fig. 1c and d, there are several
remarkable pulsive waves during one cardiac cycle in
the resultant velocity signals, two pulsive waves(slow positive pulse and succeeding steep negative
pulse) being commonly obtained around end-systole
for both healthy subjects and patients with myocardial
fibrosis, but their powers were reduced in the patients(Kanai et al. 1996). These pulsive waves cannot berecognized in standard B-mode echocardiography, Mmode echocardiography, or in TDI. The physiologicalmeanings and the mechanism of the pulsive waves
have not been previously investigated at all. Herein,
to consider the mechanism of these waves, the timingof the pulsive waves is simultaneously measured at
the multiple points in the IVS and the LV posteriorwall (LV-PW). For this purpose, it is necessary todetect the minute time-delay of several ms in thepulsive waves. If the mechanism of the pulsive waves

METHOD
Principle of measurement of heart wall vibrations withtracking
RF pulses with an angular-frequency of ␻ 0 ⫽ 2 ␲ f 0
are transmitted at a time interval of ⌬T from an ultrasonic transducer on the chest surface. The ultrasonicpulse, reflected at an object with the depth x, is received
by the same transducer. The phase difference ⌬ ␪ ( x; t)between the received signal y( x; t) and the subsequently
received signal y( x; t ⫹ ⌬T) is given by:⌬ ␪ 共 x; t兲 ⫽ ␪ 共 x; t ⫹ ⌬T兲 ⫺ ␪ 共 x; t兲⫽2␻0⌬x共t兲,
c0(1)

where ⌬x(t) ⫽ x(t ⫹ ⌬T) ⫺ x(t) is the movement of
the object during the period ⌬T from a time t and c 0 is
the acoustic velocity in the human body. By dividing the
movement ⌬x by the period ⌬T, the average velocity␷ (t ⫹ ⌬T/ 2) of the object during the period ⌬T is givenby:冉

␷ˆ t ⫹

冊

⌬T
⌬x共t兲
⫽
2
⌬T
⫽

ˆ␪ 共 x; t兲c0 ⌬,2 ␻ 0 ⌬T(2)

ˆwhere the phase difference ⌬␪( x; t) is accurately determined by the constraint least squares approach based on
the complex cross-correlation between y( x; t) and y( x;t ⫹ ⌬T) for suppressing noise components, under theconstraint that the signal waveform is invariant during⌬T but only the signal phase can change (Kanai et al.
1996). By multiplying the resultant velocity ␷ˆ (t ⫹Myocardial velocity distribution ● H. KANAI and Y. KOIWA

485⌬T/ 2) by the period ⌬T, the next depth x̂(t ⫹ ⌬T) is
estimated by:冉x̂共t ⫹ ⌬T兲 ⫽ x̂共t兲 ⫹ ␷ˆ t ⫹

冊

⌬T
⫻ ⌬T.
2

(3)

By moving the depth of the object along the direction of
the ultrasonic beam based on the resultant object depthx̂(t ⫹ ⌬T) by ␷ˆ (t ⫹ ⌬T/ 2) ⫻ ⌬T, the displacement of
the object is successfully tracked, and then the velocity
signal ␷ˆ (t ⫹ ⌬T/ 2) on the tracked large motion isaccurately estimated (Kanai et al. 1996). This procedure
is called the phased tracking method.
Limit in the number of scan lines from the ultrasonicprobe
The time-domain complex cross-correlation technique is employed in this paper to maintain the spatial
resolution, but it suffers from aliasing. In eqn (2), thephase difference during the pulse repetition interval, ⌬T,must be less than ␲ to avoid aliasing. Therefore, theupper limit in the velocity measurement, 兩␷max兩, is determined by:兩 ␷ max兩 ⬍

c 0␲
c0
⫽
⫽ 0.77 m/s.
2 ␻ 0⌬T 4f 0⌬T

Fig. 3. A diagram illustrating simultaneous measurement of thevelocity signals at multiple points on the LV wall by selecting
10 scan lines with directions {␪k } from a sector scanner inreal-time using a microcomputer.

(4)

In a typical case of ⌬T ⫽ 167 ␮s and f 0 ⫽ 3 MHz, theupper limit 兩␷max兩 is equal to 0.77 m/s.
To measure the velocity signals simultaneously at
multiple points along the surface of the LV, the ultrasonic diagnostic equipment was modified so that N scanlines with directions { ␪ k } (k ⫽ 1, 2, . . . , N) from a
sector scanner are arbitrarily selected in real time using a
microcomputer, as shown in Fig. 3, where { 䡠 } denotes
set. In the employed phased-array ultrasonic probe, thedirection of the ultrasonic beam in the fan-shaped region
is identified by inputting the beam address, n k , which isnumbered from 0 to 239, into an 8-bit address register,which controls the direction ␪k of the k-th scan line fromthe phased-array ultrasonic probe. The number, N, of thedirections should be increased as much as possible so as
to increase the spatial resolution. For the heart wall,
however, it is not easy to increase the number, N, of thetransmission directions of the ultrasonic beams to definitely display the spatial distribution of the velocity on
the cross-sectional image, as described below.
When N directions are selected from the above 240
addressable directions, the equivalent transmitted interval is lengthened to N ⫻ ⌬T from the repetition transmitted interval ⌬T of the ultrasonic pulses, and the upper
limit of the measurable velocity in eqn (4) is reduced to:兩 ␷ max,N兩 ⫽兩 ␷ max兩
c0⫽.
N
4f 0⌬TN(5)

The maximum value of the velocity at the points in the
IVS or the LV-PW of the human heart is about 0.07 m/s(Kanai et al. 1996) in a typical case, which is about 1/10
of 兩␷max兩 in eqn (4). The maximum depth, d max, of thehuman LV-PW is about 120 mm from the chest surface.
Therefore, the transmission interval ⌬T of the ultrasonicpulses cannot be shorter than 2d max/c 0 (⫽ 156 ␮s).
Thus, we must select 10 appropriate directions (N ⫽ 10)from the 240 directions addressable in the phased-arrayultrasonic probe.
Let us consider the case where the number of thedirections of the ultrasonic beams is equal to N at themeasurement. If the addresses of the beams are assignedin the order of:n1, n2, n3, . . . , nN, n1, n2, n3, . . . , nN, n1, n2, n3, . . .
兩4OOOOOO3兩4OOOOO3兩4OOOO ,
N⌬T
N⌬T
(6)
the equivalent pulse repetition interval at each direction
lengthens to N ⫻ ⌬T. Therefore, the upper limit of eqn(4) becomes 兩␷max兩/N, as described in eqn (5).

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Alternatively, for the procedure in which the transmission order of the beam is assigned as:Volume 27, Number 4, 2001

side to the LV side of the IVS and about 12 points,{B k, j } (k ⫽ 1, 2, . . . , 10), from the endocardium to then 1, n 1, n 2, n 2, n 3, n 3, . . . , n N⫺1, n N⫺1, n N, n N, n 1, n 1, n 2, n 2, . . .
兩4O3兩4OOOOOOOOOOOOOOOO3兩43兩4OOO ,⌬T
共2N ⫺ 1兲⌬T⌬T

the ultrasonic pulse is transmitted twice in every direction to determine the displacement of the object from thephase shift during ⌬T. This procedure is employed inconventional color Doppler imaging and TDI. However,there are two kinds of equivalent pulse-repetition intervals, ⌬T and (2N ⫺ 1) ⫻ ⌬T. Thus, the measurable
upper limit of the velocity is reduced to 兩␷max兩/(2N ⫺ 1),
which is about half of 兩␷max,N 兩 in eqn (5). For the tracking
operation in eqn (3), such error in the velocity estimatedin the longer interval of (2N ⫺ 1) ⫻ ⌬T accumulates in
one cardiac cycle and introduces serious errors. Therefore, we employ the transmission order of eqn (6) in invivo measurements in the following sections.
Because the frequency components up to 100 Hz
are significant in the novel diagnosis of the myocardium(Kanai et al. 1996, 1997) and the velocity signal on theheart wall is not stationary, the sampling frequency of thevelocity signal should be higher than 200 Hz. By thetransmission order of eqn (6), the equivalent sampling
frequency is 1/(N ⫻ ⌬T), as shown in Fig. 4a and about
600 Hz, which satisfies the above conditions when ⌬T ⫽167 ␮s and N ⫽ 10. Note that, even by this procedure,a time lag of ⌬T is caused in the sampling timing
between the velocity wave ␷k (t) in the k-th direction and␷k⫹1 (t) in the (k ⫹ 1)th direction and, for TDI, as shownin Fig. 4b, the time lag caused in the sampling timing
between ␷k (t) and ␷k⫹1 (t) is equal to 2M ⫻ ⌬T and ismuch larger, where M ⫻ N is the number of the beam
directions in the conventional TDI.
When all conditions are considered to be satisfied,the number, N, of the transmission direction of the ultrasonic pulses should be carefully confirmed to be 10,
which is much less than the number employed in theconventional color Doppler method or TDI (i.e., M ⫻N) which is more than 100.
RESULTS
By applying the phased tracking method describedin the previous section to each j-th point preset along thek-th scan line of 10 directions, the velocity signals at
about 12 points, {A k, j } (k ⫽ 1, 2, . . . , 10), from the RV(7)epicardium in the LV-PW of a 21-year-old healthy malevolunteer (subject N A ) were simultaneously measured. In
the in vivo experiments, the employed pulse repetitioninterval ⌬T and the ultrasonic frequency f 0 were 167 ␮s
and 3 MHz, respectively. That is, the original pulserepetition frequency (PRF ⫽ 1/⌬T) was 6 kHz. The
sampling frequency f s in the A/D conversion of thequadrature demodulated US signal was 2 MHz.
Figure 5a shows the original cross-sectional
B-mode image along the parasternal short-axis of the LV
chamber at the timing of the R-wave of the electrocardiogram (ECG). The overlaid curved broken lines show
the surfaces of the IVS, LV-PW, and the right ventricular(RV) wall. The ultrasonic beam was transmitted in 10
directions every 10th address from n 1 ⫽ 80 to n 10 ⫽170. The 40 white dots in Fig. 5a show a portion of themeasurement points on the RV side and LV side of theFig. 4. The sampling timing and delay time between the digitalized velocity signals ␷k (n) in the k-th direction when thenumber, N, of beam directions in the proposed method is 10
and ⌬T ⫽ 167 ␮s. The product M ⫻ N shows the number ofbeam directions in conventional TDI and is assumed to be 100
in this paper (M ⫽ 10). (a) By the method proposed in thispaper; (b) by the conventional TDI method.

Myocardial velocity distribution ● H. KANAI and Y. KOIWA

Fig. 5. (a) Original cross-sectional short-axis image of the LVof a 21-year-old healthy male volunteer (subject N A ) at thetiming of the R-wave. The broken lines show the surface of the
IVS and the LV-PW. Forty measurement points on the beams
from the first to 10th address are also shown by white dots. (b)Reconstructed cross-sectional image of 10 directions of ultrasonic beams at the timing T R of 6.7 ms after the R-wave.

IVS and the endocardial and epicardial sides of the
LV-PW. Figure 5b shows the cross-sectional image reconstructed from the amplitude of the A/D converted
data in each of 10 directions of ultrasonic beams at atiming of 6.7 ms after the R-wave. In this figure, the six
dots from A 1,1 to A 10,16 and the six from B 1,1 to B 10,13
show the initial positions of the tracking points on theborders at the timing of end-diastole.
Figure 6 shows a typical example of the tracking
results and the velocity signals at the four points in thesixth direction of the ultrasonic beam. Each depth of thefour points, A 6,1 and A 6,12 on the RV and LV sides of the
IVS and B 6,1 and B 6,12 on the endocardial and epicardialsides of the LV-PW, was manually preset at the timing of
the R-wave. The tracking results { x̂(t; A 6, j )} and { x̂(t;B 6, j )} of these four points ( j ⫽ 1, 12) are overlaid on
the M-mode image, as shown in Fig. 6a. Their velocity
signals, { ␷ˆ (t; A 6, j )} and { ␷ˆ (t; B 6, j )}, at these four
points are shown in Fig. 6d, e, f and g, respectively. The

487

Fig. 6. In vivo experimental results of the LV vibrations atpoints A 6,1 , A 6,12 , B 6,1 and B 6,12 along the 6th ultrasonicbeam for the same subject (subject N A ) as in Fig. 5. (a) Fourtracking results x̂(t; A 6,1 ) and x̂(t; A 6,12 ) of the IVS, x̂(t; B 6,1 )and x̂(t; B 6,12 ) of the LV-PW overlaid on the M-mode image,(b) ECG, (c) phonocardiogram (PCG), (d)(e) the velocity signals ␷ˆ (t; A 6,1 ) and ␷ˆ (t; A 6,12 ) of the IVS, (f)(g) the velocity
signals ␷ˆ (t; B 6,1 ) and ␷ˆ (t; B 6,12 ) of the LV-PW; T R -enddiastole and the display timing in Fig. 7; T II-the peak timing in
the power of the second heart sound; T⬘II-the display timing in
Fig. 11.)

resultant velocity signals were reproducible for twoheartbeats. It has already been experimentally confirmedthat these velocity components measured by the phased
tracking method are reproducible in the frequency range
from d.c. to 100 Hz (Kanai et al. 1996). Such rapid andsmall velocity components still cannot be observed byconventional ultrasonic equipment. During systole, thesignals { ␷ˆ (t; A k, j )} and { ␷ˆ (t; B k, j )} have velocity components, so that the LV lumen contracts. At the beginning of diastole, on the contrary, they have velocity
components so that the LV lumen expands.
The same tracking operation was applied to all of
about 240 points {A k, j , B k, j } (k ⫽ 1, 2, . . . , 10, j ⫽ 1,
2, . . .) preset at the timing of the R-wave at equal intervals of 385 ␮m (⫽ c 0 / 2f s ) in the IVS and LV-PW along

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each of the scan lines from n 1 to n 10 . For each of about
240 points, the velocity signals { ␷ˆ (t; A k, j )} and { ␷ˆ (t;B k, j )} were obtained.
The direction of the scan line of n 6 in Fig. 5 wasalmost always perpendicular to the movement of bothheart walls during one cardiac cycle, and the points{A 6, j } and {B 6, j } along the beam traced their movements. For the points along the beam other than n 6 ,however, it was difficult to precisely trace the movementof the same region in the heart wall over time during one
heartbeat because the direction of the ultrasonic beam
was always fixed, but the heart chamber contracted during systole and expanded during diastole. Thus, thepoint, the depth of which was preset at the R-wave,
slipped off the ultrasonic beam during systole. In a strict
sense, therefore, each of the velocity signals { ␷ˆ (t; A k, j )}and { ␷ˆ (t; B k, j )} (k ⫽ 6) does not continuously reveal
the accurate movement of each point for one cardiac
cycle. However, for the short period of every several tens
of ms, we can assume that these points stay at the same
region in the heart wall. For example, during 30 ms, aregion with an average speed of 0.03 m/s moves by 0.9mm, which corresponds to the size of the focal area ofthe ultrasonic beam in the myocardium.
By the phased-tracking method we have developed,
some discriminative pulsive waves have been found at
end-systole, as shown in Fig. 1c and d, and their Fourier
power spectra have potential for use in diagnosis of theheart (Kanai et al. 1996). At end-diastole, on the other
hand, by applying the Fourier analysis to the signal, it
has been experimentally found that a frequency component around 30 Hz is superior. In this study, therefore,
the spatial distribution of these velocity signals wasanalyzed at end-diastole and end-systole, as described
below.
For eigenvibration at end-diastole
Figure 7 shows a typical example of the wavelets ofthe simultaneously measured velocity signals { ␷ˆ (t;A k, j )} (k ⫽ 1, 2, . . . , 10) in the IVS and { ␷ˆ (t; B k, j )}in the LV-PW, respectively, at end-diastole. The central
vertical axis in each wavelet shows a timing of T R 6.7 ms
after the R-wave in Fig. 6. Each amplitude of the velocity
has already been manually corrected by dividing it by thecosine of the angle between the ultrasonic beam and thevector from the center of the LV at end-diastole to themeasurement point in the heart wall. As shown in thesewavelets, the waveforms gradually varied according to
the directions of the ultrasonic beams at the timing of T R .
Along the left-hand side of Fig. 7, each point in the IVS
and LV-PW moved upward towards the ultrasonic probe
while, along the right-hand side of Fig. 7, each point had
an opposite motion (i.e., a downward velocity component).

Volume 27, Number 4, 2001

Fig. 7. The vibration velocity signals { ␷ˆ (t; A k, j )} and { ␷ˆ (t;B k, j )} (k ⫽ 1, 2, . . . , 10) at end-diastole of T R in Fig. 6(subject N A ) in the IVS (top) and LV-PW (bottom), respectively, along the scan lines in each of 10 directions.

Each instantaneous value of the velocity at the timing T R is color-coded and the spatial distribution isdisplayed on the B-mode image in Fig. 8a. As shown in
Fig. 4a, in a strict sense, a time lag of (k ⫺ 1)⌬T ⫽ (k ⫺1) ⫻ 167 ␮s is hidden in the sampling timing of thevelocity wave in the k-th direction of the scan lines (k ⫽1, 2, . . . , 10), where ⌬T ⫽ 167 ␮s. To simulate conventional TDI, on the other hand, Fig. 8b shows thecolor-coded instantaneous value of the velocity, but an
extra time lag of (k ⫺ 1)2M⌬T ⫺ (k ⫺ 1)⌬T ⫽ (k ⫺1)(2M ⫺ 1)⌬T ⫽ (k ⫺ 1) ⫻ 2667 ␮s is added to thesampling timing of the points along the kth scan linefrom the points along the first scan line (k ⫽ 1), as shownin Fig. 4b, where ⌬T ⫽ 167 ␮s and M ⫽ 10. There isa rapid change in the polarity of the velocity waveform,as shown in Fig. 8a, especially in the IVS. By conventional TDI, however, these instantaneous motions cannot
be precisely displayed in Fig. 8b.
Moreover, to detect the spatial distribution of thephase of the eigenvibration components, the Fouriertransform was applied to each wavelet of { ␷ˆ (t; A k, j )}and { ␷ˆ (t; B k, j )} in Fig. 7 after the Hanning window witha length of 35 ms was multiplied by each wavelet. The
resultant instantaneous phase values at a frequency f 0 ,{ ␾ (t; A k, j )} and { ␾ (t; B k, j )} (k ⫽ 1, 2, . . . , 10) arecolor-coded and shown in Fig. 9a. The frequency f 0 was
set at 23 Hz because the power spectrum has a peak at f 0 ,which corresponds to the experimental values of theeigenfrequency of the human heart at end-diastole(Honda et al. 1998). In the phase values { ␾ (t; B k, j )} andMyocardial velocity distribution ● H. KANAI and Y. KOIWA

Fig. 8. Spatial distribution of color-coded velocity value of themeasured wavelets at end-diastole (T R in Fig. 6 of healthy
subject N A ) on short-axis image corresponding to Fig. 7 (subject N A ). (a) By the method proposed in this paper; (b) by theconventional TDI method.

{ ␾ (t; B k, j )}, the time lag of (k ⫺ 1)⌬T in measurementsof { ␷ (t, A k, j )} and { ␷ (t, B k, j )} along the k-th scan line
compared to measurements of { ␷ (t, A 1, j )} and { ␷ (t,B 1, j )} along the first scan line was corrected before thephase values were displayed.
As illustrated in the upper right of Fig. 9a, the value
shows the phase delay of the measured wavelet when thecosine wave of 23 Hz is fitted. Both in the IVS and the
LV-PW, the phase values vary from cyan (downward
pulse) at the right-hand side, through blue and violet, tored (upward pulse) at the left-hand side. That is, thespatial distribution of the phase value at this timing does
not conflict with the mode-2 eigenvibration of the LV
chamber in the leftmost portion of Fig. 2.
For the cross-sectional view along the longitudinalaxis, on the other hand, similar processing was applied tothe same subject N A and the resultant spatial distributionof the phase values at end-diastole were overlaid on thelongitudinal-axis cross-sectional image, as shown in Fig.
9b. The phase values along the eighth beam in Fig. 9b489

Fig. 9. Spatial distribution of color-coded phase value of thespectrum at 23 Hz of the measured wavelets at end-diastole (T R
in Fig. 6 of healthy subject N A ). (a) On short-axis image
corresponding to Fig. 7; (b) on longitudinal-axis image.

were similar to those along the fifth beam in Fig. 9a. On
the longitudinal-axis image in Fig. 9b, however, thephase value at the points in the IVS and LV-PW did not
greatly vary from the base to near the apex; that is, eachof these walls almost homogeneously moved on thelongitudinal-axis plane, resulting in the expansion of the
LV lumen at this timing of end-diastole.
By applying the same procedure in Fig. 9a to two
other young healthy male subjects (N B and N C ) and apatient with AS (subject P A ), the resultant spatial distributions of color-coded phase value of the spectrum of themeasured wavelet at end-diastole are shown in Fig. 10,(1), (2) and (3), respectively. The employed frequency
for N B and N C was the same as that for N A in Fig. 9 but,for patient P A , a lower frequency was employed. For
both the IVS and LV-PW of subjects N C in Fig. 10,(2)and P A in Fig. 10,(3), the spatial distributions weresimilar to those for subject N A in Fig. 9a; that is, thephase values vary from green or cyan (downward pulse)at the right-hand side, through yellow, to orange or red(upward pulse) at the left-hand side. For subject N B in

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Fig. 10. Spatial distribution of color-coded phase value ofthe spectrum of the measured wavelets at end-diastole ofother subjects. (1) 24-year-old healthy male subject N B( f 0 ⫽ 23 Hz); (2) 24-year-old healthy male subject N C( f 0 ⫽ 23 Hz); (3) 77-year-old female patient P A with AS( f 0 ⫽ 10 Hz).

Fig. 10, (1), however, the change in phase from theright-hand side to the left-hand side was not clearlyobtained for the LV-PW. For the IVS of N B , however,spatial distributions similar to those of the other subjects
were obtained.
For pulsive wave at end-systole
Figure 11 shows a typical example of the waveletsof the simultaneously measured velocity signals { ␷ˆ (t;A k, j )} (k ⫽ 1, 2, . . . , 10) in the IVS and { ␷ˆ (t; B k, j )} inthe LV-PW at the timing T⬘II of end-systole for healthy
subject N A in Fig. 6. The 10 scan lines were set on thelongitudinal-axis cross-sectional image, as shown in Fig.
9b. The central vertical-axis in each wavelet shows thetiming T⬘II 25 ms before the peak timing T II of the second
heart sound. As shown in these wavelets near the base of
the IVS, a slow upward pulse continued for about 30 ms
before the timing T⬘II ; that is, this slow pulse occurred
before the closure of the aortic valve. Then, a steep
downward pulsive wave occurred in the IVS around thetiming T⬘II at the beginning of the radiation timing of thesecond heart sound. The dip timing and the downward
amplitude (dip depth) varied gradually from the base to
the apex. That is, the downward steep pulse at the basepreceded that at the apex and its amplitude gradually

decreased from the base to the apex. In the LV-PW, thegradual first pulse in the IVS was not clearly observed. A
second steep pulsive wave was clearly obtained only at
the points near the mitral valves or the left atrium (LA)Fig. 11. Measured wavelets in IVS (top) and LV-PW (bottom)
at end-systole (T⬘II of Fig. 6 of subject N A ).

Myocardial velocity distribution ● H. KANAI and Y. KOIWA

Fig. 12. Spatial distribution of color-coded instantaneous velocity value of the measured wavelets at end-systole (T⬘II in Fig.
6 of subject N A ). (a) By the method proposed in this paper; (b)by the conventional TDI method.

along the right-hand side in Fig. 11, but the polarity was
upward.
Similar to Fig. 8a and b, the spatial distribution of
the instantaneous velocity component at the timing T⬘II isshown in Fig. 12a and b, respectively. In Fig. 12b, a time
lag was added to simulate the conventional TDI as in Fig.
8b.
To show the spatial distribution of the phase of thesteep pulsive components, the Fourier transform wasapplied to each wavelet of { ␷ˆ (t; A k, j )} and { ␷ˆ (t; B k, j )}in Fig. 11 after the Hanning window with a length of 35
ms was multiplied by each wavelet. The resultant phasevalues at a frequency of 50 Hz are color-coded andshown in Fig. 13a, where the steep pulses have their peak
power at around 50 Hz.
In the IVS represented in Fig. 13a, the phase values
varied from violet (⫺100°) near the base, through cyan(⫺180°), to green (⫺220°) near the apex, as can be seenin Fig. 13b, which shows that the distribution of the timedelay gradually increased from ⫺4.4 ms near the base to⫹2.2 ms near the apex for the downward steep pulse

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Fig. 13. (a) Spatial distribution of color-coded phase value ofthe spectrum at 50 Hz of the measured wavelets at end-systole
on longitudinal-axis image corresponding to Fig. 11 of subject
N A . Illustrations showing (b) the delay time of the downward
pulsive wave in the IVS and (c) the upward pulsive wave in the
LV-PW.

around the timing T⬘II in Fig. 11. In the LV-PW, on theother hand, the phase values varied from orange (⫹30°)
near the mitral valve, through yellow (⫹90°) and green(⫹150°) and, finally, to blue (⫹210°) near the apex asshown in Fig. 13c, where it can be seen that the timedelay of the upward pulse gradually increased from ⫹1.7
ms near the base to ⫹11.7 ms near the apex. Therefore,
it is clearly evident that there is a delay of several msfrom the base to the apex of the steep pulsive wave.
However, such a time delay is not detected in either Fig.
12a or b because only the amplitude of the velocity
waveform around the timing T⬘II is considered.
By applying the same procedure in Fig. 13a to thetwo other healthy subjects, NB and NC in Fig. 10a and(2), and two patients with AS, subject PA in Fig. 10,(3)and an 80-year-old male patient PB, similar results
were obtained for the IVS as shown in Fig. 14, (1), (2),(3) and (4), respectively. Though the frequency employed with both healthy subjects NB and NC was thesame 50 Hz as that employed with subject NA, for bothpatients PA and PB, the frequency employed was 10 Hz
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Fig. 14. Spatial distribution of color-coded phase value of the spectrum at 50 Hz of the measured wavelets at end-systole
on longitudinal-axis image of the other four subjects. (1) 24-year-old healthy male subject N B of Fig. 10a ( f 0 ⫽ 50 Hz);(2) 24-year-old healthy male subject N C of Fig. 10b ( f 0 ⫽ 50 Hz); (3) 77-year-old female patient P A with AS of Fig.
10c ( f 0 ⫽ 15 Hz); (4) 80-year-old male patient P B with AS ( f 0 ⫽ 15 Hz).

ease were higher at 50 Hz. There is a clear time delayof several ms for the propagation of the negative pulse
from the root of the aortic valve near the base to theapex side in the IVS. Especially for subjects NB and NC
in Figs. 14, (1) and (2), from the root of the aortic
valve (marked by white arrow), the pulsive wave
propagates radially in the IVS. For the LV-PW, however, the pulsive signals were not clearly detected inthese subjects other than NA.
For irregular vibrations in the ejection period of patientswith AS
The proposed method was applied to IVS and
LV-PW along each of 10 scan lines set on the longitudinal axis cross-sectional image of patient P A with AS.
Acquired aortic valve stenosis often results from progressive degeneration and calcification of a congenitally
defective bicuspid valve. Figure 15 shows the tracking
results and velocity signals of the four points on bothsides of IVS and LV-PW. AS leads to LV hypertrophy

and LV ischemia. The IVS became thickened to about 18
mm in patient P A , as shown in the M-mode of Fig. 15a.
Generally, one of the clinical features of AS is a systolic
thrill at the base of the heart and a mid-systolic murmur,
which was obtained in Fig. 15c, in the aortic area (Forbes
and Jackson 1997). By the in vivo experiments in thisstudy, moreover, noisy vibration signals, especially in
the IVS in the ejection period, were observed for the firsttime, as shown in Figs. 15d and e. These noisy components are caused by the irregular blood flow in the
stenotic aortic area.
Each of Figs. 16, 17 and 18 shows the waveforms of
the simultaneously measured velocity signals { ␷ˆ (t;A k, j )} (k ⫽ 1, 2, . . . , 10) in the IVS and { ␷ˆ (t; B k, j )}in the LV-PW in the ejection period of healthy subject
N A , and of patients P A and P B , respectively. The centerof the vertical axis in each waveform was determined by
the mid-systolic timing of T sys ⫽ (T R ⫹ T II )/ 2, where
T R and T II are the peak timing of the R-wave and thesecond heart sound, respectively, as shown in Fig. 15.

Myocardial velocity distribution ● H. KANAI and Y. KOIWA

Fig. 15. In vivo experimental results of the LV vibrations atpoints A 8,1 , A 8,24 , B 8,1 and B 8,23 along the 8th ultrasonicbeam for the same patient (P A ) with AS as in Figs. 10,(3) and14,(4). (a) M-mode image and four tracking results x̂(t; A 8,1 )and x̂(t; A 8,24 ) of the IVS, x̂(t; B 8,1 ) and x̂(t; B 8,23 ) of the
LV-PW overlaid from top to bottom; (b) ECG; (c) phonocardiogram (PCG); (d)(e) the velocity signals ␷ˆ (t; A 8,1 ) and ␷ˆ (t;A 8,24 ) of the IVS; (f)(g) the velocity signals ␷ˆ (t; B 8,1 ) and ␷ˆ (t;B 8,23 ) of the LV-PW.

For healthy subject N A of Fig. 16, at the points near
the LV lumen of IVS and LV-PW, there were highfrequency components in the velocity signals during theejection period. These components are due to the rapid
blood flow during the ejection period. For patient P A of
Fig. 17, high-frequency components were observed at
the points near the LV-PW endocardium, but at points
almost in the IVS. For patient P B of Fig. 18, especiallynear the root of the aortic valve of the base in the IVS,
there were large noise components with high-frequency
components around 100 Hz.
To quantitatively evaluate the power difference between the observed positions, 16 points were selected on
the four layers of the RV side of IVS, the LV side of IVS,
the LV-PW endocardium, and the LV-PW epicardium
along the beams from the fourth to seventh scans, as
enclosed by rectangles in Figs. 16, 17 and 18. By applying the Fourier transform to each signal at these 16 points
in each of Figs. 16, 17 and 18, after multiplication by the
Hanning window with a length of two or three hundreds
ms, the power spectrum was obtained. The employed
Hanning window is shown at the top of each column inthese figures. By averaging the resultant power spectra at
the points in each of the four layers, the results are shownin Fig. 19 (1), (3) and (4), respectively. By applying the493

Fig. 16. Measured velocity signals along longitudinal-axis in
IVS (top) and LV-PW (bottom) in ejection period of the same
healthy subject (N A ) as in Figs. 5–9 and 11–13. The signals
enclosed by rectangles in four layers are employed in Fig. 19afor evaluation of the averaged power spectra.

same procedure to healthy subject N B , the result isshown in Fig. 19, (2).
For healthy subjects (N A and N B ) in Fig. 19, (1) and(2), the low-frequency components around d.c. werelarge for both walls (IVS and LV-PW). At the same time,
there were large power differences between the twolayers in both walls, which shows that the change inthickness generated in each wall during the ejection
period was large; for the IVS of P A in Fig. 19, (3),however, the power was large. However, the power andpower difference were not so large for the LV-PW of P A
in Fig. 19 (3) nor for either wall of P B in Fig. 19 (4).
With regard to the high-frequency components inthe signals of Fig. 17, for healthy subject N A in Fig. 19(1), the power spectrum at the point near the LV lumenof IVS and LV-PW had larger power in the frequency
ranges from about 100 Hz to 120 Hz and from about 140
Hz to 180 Hz. The power spectra at the RV side of IVS
and at the LV-PW epicardium were roughly similar.
Similar results were obtained for subject N B in Fig. 19(2). Although for patient P A in Fig. 19 (3), the RV sideof IVS had a power spectrum similar to that of the LVside of IVS and the LV-PW endocardium. For patient P B
in Fig. 19 (4), the LV side of the IVS had a much larger
power than the RV side of IVS. For both patients with
AS, the power of the velocity signals in IVS was at least
5 dB larger than that in both healthy subjects N A and N B
in the frequency range from 30 Hz to 200 Hz.

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Fig. 17. Measured velocity signals along longitudinal-axis in
IVS (top) and LV-PW (bottom) in ejection period of the same
female patient (P A ) with AS as in Figs. 10,(3), 14,(3), and 15.

DISCUSSION
In this study, for each of about 20 points preset in
the IVS and LV-PW along each of 10 scan lines, thevelocity waveform was measured continuously for a few
heartbeats. By applying the Fourier transform to thevelocity wave, the power spectrum was obtained up to
100 Hz and the phase value at the frequency with thepeak power was color-coded and displayed. The powerof the high-velocity components up to several tens of Hz
was less than 1/30 in amplitude of that of the large slow
motion up to 10 Hz due to heartbeat. The wide dynamic
range in amplitude up to 100 Hz was achieved in themeasurement (Kanai et al. 1996).
When the instantaneous velocity is color-coded anddisplayed as a 2-D image, as shown in Figs. 8a and 12a,the results highly depend on the timing of the sampling.
In the phase value at the peak frequency, however, thephase values were averaged during the period of thewindow length (35 ms) employed in the Fourier transform. Thus, the results did not highly depend on thetiming. Moreover, the time lag in the scanning of thebeam was corrected in Figs. 9 and 13a.
The large slow motion, on the order of several
hundred ␮m up to 10 Hz, is displayed by conventional
TDI. However, the displacement of each point is nottracked. For rapid small motion, on the order of several
tens of ␮m up to 100 Hz, conventional TDI cannot

Volume 27, Number 4, 2001

Fig. 18. Measured velocity signals along longitudinal-axis in
IVS (top) and LV-PW (bottom) in ejection period of the same
male patient (P B ) with AS as in Fig. 14,(4).

display it because the sampling frequency is about 30 Hz.
In this study, the motion was tracked and accurately
measured at a sampling frequency of 600 Hz, and its
spatial distribution was displayed by restricting the number of the beam directions to 10 so as to avoid aliasing.
From the in vivo experiments, various results wereobtained. For end-diastole, the phase values of the points
along the fifth beam in the short-axis image in Fig. 9awere similar to those along the eighth beam in thelongitudinal axis image in Fig. 9b. From these resultsfrom separate experiments, the promise of the measurements was confirmed.
The distribution of the phase value at 23 Hz in Fig.
9a and the instantaneous velocity values in Fig. 8a showthat there was a mode-2 eigenvibration in the short-axis
image, which has not been observed in conventional TDI
methods. The reasons why such eigenvibration was excited, for example, by the blood flow at atrial systole,
should be considered in the future.
For end-systole, on the other hand, the spatial distribution of the phase values of the pulsive wave which
we found in the previous study (Kanai et al. 1996) at
end-systole was definitely displayed for the first time in
Fig. 13. The mechanism of the pulsive wave generated at
end-systole should also be investigated in the future by invitro and in vivo experiments. There are two possibilities:
the propagation of the pulsive wave caused by the clo-

Myocardial velocity distribution ● H. KANAI and Y. KOIWA

Fig. 19. Power spectra of measured velocity signals in ejection
period averaged in the points from the fourth scan line toseventh scan line in each of four layers. left-hand side: for theRV-side of IVS (squares) and LV-side of IVS (crosses); righthand side: for LV-PW endocardium-side (crosses) and LV-PW
epicardium-side (squares). (1) For healthy subject N A in Fig.
16; (2) For healthy subject N B in Fig. 14,(1); (3) For patient P A
with AS in Fig. 17; (4) For patient P B with AS in Fig. 18.

sure of the aortic valve and the time difference in the
depolarization in each regional myocardium. For theformer case, the propagation speed of the 50 Hz component was about 5 m/s in both IVS and LV-PW for healthy
subject N A in Fig. 13a because the distance from thebase-side to the apex-side is 34 mm in IVS and 50 mm
in LV-PW, and the delay is 6.6 ms in IVS and 10 ms in
LV-PW. For the other healthy subjects, N B and N C in
Fig. 14, (1) and (2), the propagation speed was also about
5– 6 m/s. For patients P A and P B in 14, (3) and (4),however, the propagation speed of 10 Hz component was
about one-tenth of the above value.
For patients with AS, it is well known that a murmur is radiated especially at systole (Constant 1985).
However, the original vibration of the heart sound cannot
be directly detected from the chest surface using a stethoscope or a microphone. In this study, the myocardial
vibration that corresponds to the murmur was directly
detected for the first time. The spatial distribution of the
myocardial irregular vibration should be investigated in

495

more detail by increasing the number of patients. Moreover, the effects of the irregular vibration on the heart
function and the myocardium should be clarified in the
future because it is already known that the actuatedvibration on the order of several tens of Hz in systole
rapidly affects the contraction of the myocardium (Janssen et al. 1996; Koiwa et al. 1997).
Further possible applications of the technique proposed in this paper are as follows:
1. The different transmural layers of the myocardium
have transmural heterogeneity with respect to themicrovascular flow, metabolic consumption and thestrength of contraction. The method developed in thisstudy can reveal the intramyocardial contraction/relaxation heterogeneity by evaluating the change inthickness or its speed in two dimensions.
2. By in vivo experiments represented in Figs. 8a and 9a,
the mode-2 vibration was confirmed. Thus, using thismode, the end-diastolic pressure and the average elastic property of the heart wall can be obtained, as
described in the Introduction.
3. A discriminative pulsive wave at end-systole wasfound in the measured velocity waveform in our previous study (Kanai et al. 1996). The power spectra ofpatients with fibrosis were different from those ofhealthy subjects. The origin and the mechanism of thepulsive wave should be investigated continuously,
based on the method developed in this paper for thedevelopment of a novel method of diagnosis.
The following problems remain to be solved:
1. In the velocity measurement employed, based on the
cross-correlation between the quadrature-demodulated signals of the succeedingly received signals,
spatial averaging of the phase shifts due to the displacement around each measurement point is unavoidable. As described in the Introduction, the minimum interval between the succeeding points presettable in the heart wall is determined by the original
frequency and bandwidth and is about 500 ␮m in thesystem. In this paper, we have assumed that the velocity is spatially constant in the region, with a widthof 500 ␮m around each measurement point. For increasing precision in measurement of the velocity anddisplacement, it will be necessary to consider thevelocity gradient, even in each small region, in thenext stage of the research.
2. It is reasonable to consider that each ultrasonic beam
passes through the same myocardium for a shortperiod of several tens of ms. However, during one
cardiac cycle, it is difficult to track the movement of
the myocardium because the direction of the movement does not always coincide with the direction of
the ultrasonic beam. To overcome this problem, tracking operation in 2-D or 3-D will be necessary.

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In the literature, by transmission of multiple ultrasonic beams, the lateral flow component is determined by correlation using a dual-beam probe (Weiqi and Lin-xin 1982; Overbeck et al. 1992; Routh etal. 1990) or a two-sector transducer probe (Dotti et al.
1992). However, it is not easy to apply these techniques directly to the heart wall, which has complex
structure.
In the optical flow technique (Horn and Schunck1981), cardiac contractility is assessed by decomposing the overall heart wall motion into translation,
rotation, deformation and contraction components ofthe cardiac muscle (Mailloux et al. 1987; Meunier etal. 1989). This method requires extremely long computation time and the decomposed motion components, which are based on the direction of the contrast
brightness, are limited to large and slow, which can berecognized in the B-mode image.
In frame-to-frame 2-D correlation analysis ofspeckle patterns in B-mode images, the lateral andaxial components of the 2-D tissue slow motion (Robinson et al. 1982; Trahey et al. 1986; Akiyama et al.
1988; Bohs and Trahey 1991; Chen et al. 1992) orblood flow (Bohs and Trahey 1991; Trahey et al.
1988; Ramamurthy and Trahey 1991) have been assessed. Morsy and von Ramm (1999) tracked tissue
motion and blood flow in 3-D by a similar correlation
technique. The size of the employed correlation window is coarse, on the order of tens of mm. In thesemethods, the axial resolution is limited by the center
frequency and bandwidth of the US. The lateral resolution is limited by the actual beam-width and thespacing interval of the A-scans. For LV-PW, thetypical depth, d, is about 120 mm from the chest
surface. The finest lateral resolution r at the LV-PW
is d tan{( ␲ / 2)/ 240} ⬵ d( ␲ /480) ⫽ 785 ␮m, when
240 ultrasonic beams are scanned by a sector-typeprobe in the 90° range. The achievable lateral resolution is still coarse in the measurement of rapid motion
with an amplitude of several ␮m. Moreover, the typical video frame rate in the 2-D imaging system is on
the order of 1/30th of a s. Thus, the acquisition rate islimited to at most on the order of 30 Hz, which is too
slow to detect the rapid components. Therefore, themeasurement of rapid velocity components in 2-D or
3-D is currently still difficult to realize.
3. Though typical timings have been selected on theorder of a few ms, and are displayed in Figs. 8a, 9, 10,12a, 13a and 14, a continuous display of the 2-D
distribution of the instantaneous amplitude and phasewould be more effective.
4. In the determination of the propagation delay of thediscriminative pulsive wave or irregular vibration due
to blood flow among different transmural layers of theVolume 27, Number 4, 2001

myocardium along a beam direction, the delay time issmaller than that obtained among the different directions of the ultrasonic beam in Fig. 13a. It should bepossible to determine accurately such small delay
time in the frequency domain using high-frequency
components up to 100 Hz.
SUMMARY
In this paper, we have modified a conventional
ultrasonic diagnostic system to allow 10 scan lines froma sector scanner to be selected arbitrarily for measurement and analysis, so that the velocity signals can be
simultaneously measured at multiple points in the IVS
and the LV wall for imaging of their spatial distribution.
By applying this method to healthy subjects andpatients with AS in this study, we obtained spatial distributions of small vibrations that were superimposed on
the B-mode image. From the results at end-diastole, we
confirmed that there is mode-2 eigenvibration on the LV
wall. For end-systole, the time delay in the propagationof the steep downward pulses from the root of the aortic
valve near the base to the apex can be definitely detected.
Moreover, for the ejection period of the patients with AS,
irregular vibration components, which correspond to thesystolic murmur and have large power, were detected.
This method offers potential for imaging of the spatial
distribution of small vibrations with high-frequency
components, which cannot be recognized by conventional B-mode echocardiography, M-mode echocardiography or by TDI. The method developed herein has
potential for application to many patients with various
kinds of heart diseases in the near future.
Acknowledgements—The authors are grateful to Prof. Emeritus
Noriyoshi Chubachi and Prof. Emeritus Motonao Tanaka of Tohoku
University, Prof. Floyd Dunn of the Bioacoustics Research Laboratory,
the University of Illinois, Prof. Kunio Shirato and Hide-ichi Kamada of
Tohoku University School of Medicine, and Dr. Hideyuki Honda of
Touhoku Bunka Gakuen University, for helpful discussions. The authors also acknowledge the contributions of Shigemitsu Nakaya and
Hideyuki Hasegawa of our laboratory for their support of in vivo
experiments. This work was supported in part by a Grant-in-Aid for
Scientific Research from the Ministry of Education, Science and Culture of Japan.

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