Jpn. J. Appl. Phys. Vol. 38 (1999) pp. 3403–3408
Part 1, No. 5B, May 1999c
°1999
Publication Board, Japanese Journal of Applied Physics

In Vivo Measurement of Small Velocity Signals and Change in Thickness of the Heart Walls
Hiroshi K ANAI ∗1 , Yoshiro KOIWA ∗2 , Yoshiko S AITO ∗3 , Ikuko S USUKIDA ∗4 and Motonao TANAKA ∗5
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan(Received November 27, 1998; accepted for publication January 18, 1999)

We have previously developed a new method for accurately tracking the movement of the heart wall based on both the phaseand magnitude of the demodulated signals to determine the instantaneous position of an object. By this method, velocity signalsof the heart wall with small amplitudes less than several micrometers on the motion resulting from a heartbeat can be accurately
detected. Moreover, the method has been applied to multiple points preset in the heart wall along an ultrasonic beam so that the
spatial distributions of the local change in thickness during one cardiac cycle is determined. In this paper, the method is applied
to the free wall of the right ventricle (RV), the interventricular septum (IVS), and the posterior wall of the left ventricle (LV).
From the relationships among the results for these parts of the heart, new findings which characterize the velocity signals andthe change in thickness in each cardiac period are described. This method offers potential for quantitative myocardial diagnosis.
KEYWORDS: velocity signal measurement, local change in thickness, myocardial contraction/relaxation, myocardial motility,
cardiac cycle

1. Introduction
In the free wall of the right ventricle (RV), the interventricular septum (IVS), and the posterior wall of the left ventricle (LV) shown in Fig. 1(a), thickening and thinning periodically occur during myocardial contraction and relaxation as
illustrated in Figs. 1(b) and 1(c). This thickening and thinning at each local area in the heart wall corresponds to theregional myocardial motility, which originates from the sliding of the myosin and actin fibers. To noninvasively realize
evaluation of this motility using ultrasound, it is necessary to
track the instantaneous positions x A (t) and x B (t) of the twopoints A and B which are preset at the end-diastole along
an ultrasonic beam in the heart wall. Then, the change inthickness, 1h AB (t), between these two points A and B fromtheir thickness, h 0 , at the end-diastole is obtained from thedifference between x A (t) and x B (t) as illustrated in Fig. 1(c)if the ultrasonic beam is almost perpendicular to the wall during the cardiac cycle.1, 2) Such noninvasive measurement of
the change in thickness of the regional area in the heart wall
during each cardiac cycle provides essential tools for the diagnosis of heart diseases.
Though M-mode echocardiography offers an advantage incritically looking at the motion pattern of the LV, its spatial
resolution along the ultrasonic beam is limited to a few wavelengths, namely, only up to 1 mm for ultrasound of 3 MHz
because an M-mode image is displayed based on the amplitude of the reflected ultrasound. On the other hand, there
have been numerous elaborate techniques proposed for noninvasive measurement of the velocity of the blood flow in theheart or the arteries based on the Doppler effect.3) Moreover,
several methods, including the phase-locked-loop (PLL) techniques, have been proposed to measure rough changes in the
diameter of the arterial walls by tracking arterial wall dis∗1 Graduate School of Engineering, Tohoku University, Sendai 980-8579,

Japan. E-mail address: hkanai@ecei.tohoku.ac.jp∗2 First Department of Internal Medicine, School of Medicine, Tohoku Uni-

versity, Sendai 980-8575, Japan.

∗3 Third Department of Internal Medicine, School of Medicine, Tohoku Uni-

versity, Sendai 980-8575, Japan.
∗4 Graduate School of Engineering, Tohoku University, Sendai 980-8579,
Japan.
∗5 Tohoku Welfare Pension Hospital, Takasago 10, Fukumuro, Miyagino-ku,
Sendai 983, Japan.

placement in real time.4, 5)
For the accurate detection of velocity signals, that is, the instantaneous movement on or in the heart wall, we have developed the following “phased tracking method”.2) This method
has been confirmed by experiments using a water tank andhas been applied to the in vivo detection of small velocity signals, with sufficient reproducibility, on the wall of the humanheart.2) The detected velocity signals show rapid motion including high frequency components with small amplitudes,
which are difficult to recognize by M-mode echocardiography.
Moreover, the method has been 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.1) From the results, by deleting the parallel component,
the thickness change components during myocardial contraction/relaxation are detected. Then, their spatial distribution is
obtained and is superimposed on the M-mode image using acolor code.
Spectrum analysis was first applied to the resultant noninvasively detected signals to identify the frequency band forthe components from 25 Hz to 90 Hz due to the myocardial
thickening and thinning. Such analysis shows the novel possibility of diagnosis of the local myocardium.1, 2)
For such waveform analysis and/or spectrum analysis,
however, it is significant to characterize each of six periods in
one cardiac cycle using the results of the velocity signals andthe change in thickness, which are measured by our method.
For this purpose, in this study, the developed method was applied to the free wall of the RV, the IVS, and the posterior wallof the LV of a healthy young male volunteer and the IVS of amale patient with dilated-cardiomyopathy (DCM). From therelationship among the results for the three heart walls and thedifferences between the subjects, new findings which characterize the velocity signals and the change in thickness in eachperiod during one cardiac cycle are described.
2. Principles of Measurement of Change in Thickness ofthe Wall
By referring to the M-mode image, which is reconstructedfrom the A/D converted data, we manually preset two points,
A and B, in the heart wall or arterial wall along an ultrasonic

3403

3404

Jpn. J. Appl. Phys. Vol. 38 (1999) Pt. 1, No. 5Bbeam at a time t0 of R-wave of the electrocardiogram (ECG)
as illustrated in Fig. 1(b). We assume that both point A andpoint B have only a velocity component which is parallel tothe direction of the beam if the direction and position of theultrasonic beam are appropriately selected so as to be perpendicular to the wall during the cardiac cycle. The principle of
the accurate detection of the change in thickness, 1h AB (t),between points A and B in the wall is briefly described asfollows.2)
2.1 For measurement of instantaneous movement 1di (t) of
object (i)RF pulses with an angular-frequency of ω0 = 2π f 0 are
transmitted at a time interval of 1T from an ultrasonic transducer. The ultrasonic pulse reflected by the object (i) is received by the same ultrasonic transducer. The output signal isamplified and quadrature-demodulation is applied to the signal. The resultant in-phase and quadrature signals for eachtransmitted pulse are simultaneously A/D converted at a sampling frequency of 1/TS , and these two signals are combined
into a complex signal, y(x; t), where x(t) and its simple ex-

H. K ANAI et al.

pression x denote the depth from the ultrasonic transducer.
The instantaneous depth xi (t) of the object, (i), from the ultrasonic transducer is given by the product of the acoustic velocity, c0 , and the instantaneous period τi (t) required for oneway transmission from the ultrasonic transducer to the object,(i). The phase θ (xi ; t) of the signal y(xi ; t) is given by the angular frequency ω0 multiplied by twice the delay time τi (t).
Thus, the phase difference 1θ(xi ; t) between the analytic signals y(xi ; t) and y(xi ; t + 1T ) of the successively received
signals in the interval 1T is given by1θ(xi ; t) = θ (xi ; t + 1T ) − θ (xi ; t)
= 2ω0 {τi (t + 1T ) − τi (t)}2ω01di (t),(1)c0where 1di (t) = xi (t +1T )−xi (t) is the instantaneous movement of the object (i) in the period 1T after a time t. Then,
1di (t) is given from the measured data by=

1di (t) = c0 ·1θ(xi ; t)
.
2ω0

(m)

(2)

2.2 For accurate determination of the phase change
1θ(xi ; t)Since it is essential to accurately determine the phasechange 1θ(xi ; t) of eq. (2) during the period 1T , the following complex correlation is introduced into the determination
procedure of the instantaneous movement of the object position xi (t).2)
Since y(x; t) and y(x; t + 1T ) are described by thedamped sinusoidal signals, the standard cross-correlation procedure does not uniquely determine the optimum movement δx of y(x; t + 1T ) from y(x; t) as theoretically described.2) To solve this problem, by restricting the magnitude of the average change β(δx ; xi ; t) from y(x; t) to y(x +δx ; t + 1T ) around xi (t) to one and replacing β(δx ; xi ; t) byexp{ j1θ(δx ; xi ; t)}, we define the normalized mean squared
difference, α(1θ; δx ), between y(xi + δx ; t + 1T ) andc i ; t) by which miniy(xi ; t). From the phase change 1θ(xmization of α(1θ; δx ) with respect to δx is achieved, the instantaneous movement of 1di (t) in eq. (2) is given bycdi (t) = c0 · 1θ(xi ; t) . (m)
(3)
1d
2ω0
di (t) by 1T , the velocity signal is given as
By dividing 1dfollows:di (t)1d. (m/s)(4)vbi (t) =1T
The velocity signal and the spectrum will be effective in diagnosis of the local myocardium.1)

Fig. 1. An illustration explaining the procedure used to measure the change
in thickness of (c) by tracking the movement x A (t) and x B (t) of points A
and B preset in one of the three heart walls along the ultrasonic beam.
(a) cross-sectional image, (b) ECG and the displacement, x A (t) and x B (t),superimposed on the M-mode image, (c) change in thickness, 1h A B (t).

2.3 For tracking of the object position xi (t)The position xi (t) of the object (i) in the heart wall changes
by more than 10 mm due to the heartbeat in one cardiac cycle. It is, therefore, necessary to track the instantaneous object
position xi (t). For this purpose, by accumulating the estimate
di (t) of the instantaneous movement in eq. (3), the next
1d
object position xbi (t + 1T ) is estimated bydi (t).
xbi (t + 1T ) = xbi (t) + 1d

(m)

(5)

Jpn. J. Appl. Phys. Vol. 38 (1999) Pt. 1, No. 5B

H. K ANAI et al.

di (t) and the next objectThus, the instantaneous movement 1dposition xbi (t + 1T ) are simultaneously determined and are
obtained as waveforms.
When the time interval, 1T , of the transmission of the RF
pulses is about 200 µs, the maximum value of the instantaneous movement 1d(t) of an object in the heart wall is about
20 µm during the time interval 1T . These values are muchless than the wavelength of about 500 µm at 3 MHz. Since
the quadrature-demodulated signals are A/D converted as asampling interval, TS , of 1 µs in this paper, the spatial resolution 1x S = TS × c0 /2=750 µm in the direction of depth.
However, the resultant estimate xbi (t) of the next object position of eq. (5) in the above procedure is represented not by adiscrete value which depends on the sampling interval TS but
by the continuous value which is determined from the phasec i ; t). Thus, accurate tracking of the object isdifference 1θ(xrealized by this method and a small instantaneous movementof micron order is determined.
2.4 For measurement of change in thickness of the wall
Let us assume that the ultrasonic beam is almost perpendicular to the wall during one cardiac cycle and that the velocity direction of each point (i) in the wall is parallel to thedirection of the ultrasonic beam. Thus, from the difference
between the instantaneous object positions xi (t) and xi +1 (t),the thickness of the local region, which is denoted by h i (t), is
obtained bybi (t). (m)(6)
hbi (t) = xd
i +1 (t) − x
The change in thickness, 1h i (t), from the initial value h i (t0 )at time t0 is obtained from the estimated velocity, vi (t) andvi +1 (t), as follows:di (t) = hbi (t) − h i (t0 )
1h
Z t
{vd
bi (t)}dt,=
i +1 (t) − v

(m)

(7)

t0

where 1di (t) = vi (t) × 1T . When the region between
the ith and (i + 1)-th points becomes thicker at time t,
1h i (t) > 0, while for the case when the region becomesthinner, 1h i (t) < 0. However, 1h i (t) depends on the distance between xi (t) and xi +1 (t). Thus, by dividing 1h i (t)by the distance |xi +1 (t) − xi (t)|, the normalized speed of thelocal change in thickness which occurs in the assumed homogeneous myocardium between points (i) and (i + 1), denotedby Si (t), is defined by
1h i (t). [(m/s)/m](8)
Si (t) =|xi +1 (t) − xi (t)|The spatial distributions {Si (t)} of the normalized speed of thelocal change in thickness are color-coded and superimposedon the M-mode image. In our papers, red corresponds to thinning of the myocardium (Si (t) < 0) and blue corresponds tothickening of the myocardium (Si (t) > 0).
3. In Vivo Experimental Results for the Heart Walls
3.1 Explanation of the procedure of the proposed method
Firstly, the proposed method is applied to the detection ofvelocity signals on the free wall of the RV, the IVS, and theposterior wall of the LV of a healthy 24-year-old male volunteer. Figures 2(e-1), 2(e-2), and 2(e-3) show the B-mode
images of these walls along the longitudinal axis, which were3405

obtained by standard ultrasonic diagnostic equipment. Multiple points {i} are set in each wall. Since the results obtainedby the proposed method depend on the angle between the direction of the velocity vector and the ultrasonic beam, the direction of the ultrasonic beam passing through these walls is
selected so that the beam is almost perpendicular to each wall,as shown in Figs. 2(e-1), 2(e-2), and 2(e-3), during the A/D
conversion of several cardiac cycles. During the acquisition
period, respiration is suspended.
Figures 2(a) and 2(b) show the ECG and the phonocardiogram (PCG), respectively. Before applying the method
described in §2, by referring to the M-mode image, which
was reconstructed from the magnitude of the digitized signalof the analytic signals, the positions {bxi (t0 )} of the multiple
points {i} in each wall are manually preset using the workstation at even intervals of 1x S =0.75 mm. The tracking results{bxi (t)}, estimated by eq. (5) of the points {i}, are superimposed on the M-mode image by white lines as shown in Figs.
2(d-1), 2(d-2), and 2(d-3).
Figures 2(c-1), 2(c-2), and 2(c-3) show the superimposed
estimates of the velocity signals {bv (xi ; t)} of each heart beaton the tracked points {bxi (t)} on the free wall of the RV, the
IVS, and the posterior wall of the LV, respectively, during 6
heartbeats. The vertical axis of these figures is inverted sothat the negative value of the velocity, which is shown above
the baseline, corresponds to the situation in which the object moves in the direction of the ultrasonic transducer on thechest wall, which is more easily understood. The resultant
velocity signals are sufficiently reproducible for six heartbeat
periods.
For the first cardiac cycle, Figs. 2(d-1), 2(d-2), and 2(d3) show the tracking results {bxi (t)} of the multiple points {i}by white lines and the normalized speed of the local change
in thickness, {Si (t)}, of eq. (8). The values {Si (t)} are colorcoded according to the coloring scheme described in §2.4, andthe results are superimposed on the M-mode image.
3.2 Discussion of the myocardial movement of the healthy
subject
From the velocity signals and the change in thickness ofFig. 2, which are first obtained by the developed method, there
are several new findings as follows, which cannot be recognized in the M-mode image of the previous standard echocardiography.
3.2.1 Atriosystolic phase
See period “A” in Figs. 2(c) and 2(d). In this period, just after the timing of the P-wave in the ECG, the blood flows into
the ventricle from the atrium through atrioventricular valves.
From the velocity signals in Figs. 2(c-2) and 2(c-3), the IVS
and the posterior wall of the LV move so that the LV expands.
For the free wall of the RV, there is a small velocity component in Fig. 2(c-1) causing the RV to expand. However, clear
movement is not recognized for the free wall of the RV as
shown in the M-mode image of Fig. 2(d-1).
In Figs. 2(d-1), 2(d-2), and 2(d-3), since there are red components in this atriosystolic phase, all three walls becomethin. Also, such change in thickness cannot be recognizedin the M-mode image.
3.2.2 Isovolumetric contraction period
See period “IC” in Figs. 2(c) and 2(d). In this period, theventricles start to contract, but the blood still does not flow

3406

Jpn. J. Appl. Phys. Vol. 38 (1999) Pt. 1, No. 5B

H. K ANAI et al.

I

i

i

i
Fig. 2. In vivo experimental results on (1) the free wall of the RV, (2) the IVS, and (3) the posterior wall of the LV of a healthy 24-year-old
male volunteer. (a) ECG. (b) PCG. (c) Superimposed estimates of the velocity signals {bv (xi ; t)} of the multiple points {i} in each of
the three heart walls. (d) The tracking results {bxi (t)} of the multiple points {i} are shown by white lines. The normalized speed of thechange in thickness, Si (t) [(m/s)/m], is mapped according to the defined color scheme and is superimposed on the tracking results.
(e) The B-mode cross-sectional images and the directions of the ultrasonic beam.

out from the ventricles to the aorta or the pulmonary artery
because the semilunar valves are still closed.
From the velocity signals in Figs. 2(c-1), 2(c-2), and 2(c-3),
it can be seen that there are some pulsive components in thisperiod in the three heart walls. The free wall of the RV andthe IVS move causing the RV to shrink. The posterior wall of
the LV has velocity components larger than those in the IVS
so that the volume of the LV decreases.
From the blue components in Figs. 2(d-1), 2(d-2), and 2(d3), the posterior wall of the LV and the IVS become slightly
thick just after the Q-wave of the ECG. About 30 ms after
this change, just after the R-wave of the ECG, the free wallof the RV also becomes slightly thick. Such movement or
the change in thickness cannot be recognized in the standard
M-mode images.
3.2.3 Ejection period
See period “E” in Figs. 2(c) and 2(d). In this period, justafter the semilunar valves open due to the increase of the innerpressure of the LV and RV, the blood in the LV and RV flows
out to the aorta or the pulmonary artery due to the contractionof the ventricles.
From the velocity signals in Figs. 2(c-1), 2(c-2), and 2(c3), it can be seen that there are velocity components withrather simple waveforms in each wall which correspond toJpn. J. Appl. Phys. Vol. 38 (1999) Pt. 1, No. 5B

x

H. K ANAI et al.

3407

i

Fig. 3. In vivo experimental results on the IVS of a 57-year-old male patient with DCM. (a) M-mode image, (b) ECG. (c) inner pressureof the LV. (d) Superimposed estimates of the velocity signals {bv (xi ; t)} of the multiple points {i} in the IVS. (e) The tracking results{bxi (t)} of the multiple points {i} are shown by white lines. The normalized speed of the change in thickness, Si (t) [(m/s)/m], ismapped according to the defined color scheme and is superimposed on the tracking results. (f) The B-mode cross-sectional image
and the direction of the ultrasonic beam.

the shrinkage of the RV and the LV.
In this period, there are clear differences in velocity among
the layers in each wall, which shows that there is a largechange in thickness in each wall. From the blue components
in Figs. 2(d-1), 2(d-2), and 2(d-3), it can be seen that there
are almost homogeneous changes in thickness in each of thethree walls.
3.2.4 Isovolumetric relaxation period
See period “IR” in Figs. 2(c) and 2(d). At the end of theejection period, the IVS and the posterior wall of the LV havepulsive velocity components with directions opposite those in
the previous ejection period indicating that the LV and RV
slightly expand and then the inner pressure of the LV and thatof the RV become lower than those of the aorta and the pulmonary artery. Therefore, due to these pulsive velocity components, the semilunar valves close at the beginning of thisisovolumic relaxation period. Thus, there are rapid decreases(red or yellow components) in the thickness of the free wall of
the RV, the IVS, and the posterior wall of the LV as shown in
Figs. 2(d-1), 2(d-2), and 2(d-3). However, these components
are not clearly recognized in the M-mode image.
Only the pulsive component of the IVS has been previously

analyzed in the time domain and the frequency domain,1, 2)
and there are clear differences in the power spectra between
normals and patients with cardiomyopathy.
At the latter half of this period, the three walls move so thatthe inner volume of the LV and that of the RV become slowly
larger.
3.2.5 Period of rapid filling
See period “R” in Figs. 2(c) and 2(d). In this period, theblood rapidly flows into the LV and the RV. Thus, each wall
has large components as shown in Figs. 2(c-1), 2(c-2), and2(c-3) and there are large differences in velocity among thepoints in the walls, that is, large changes in thickness in the
myocardium. As shown by the red or yellow regions in Figs.
2(d-1), 2(d-2), and 2(d-3), the large decrease in thickness isalmost homogeneous in each wall.
3.2.6 Period of slow filling
See period “S” in Figs. 2(c) and 2(d). In the first half of
this period, there are phenomena similar to those seen in theprevious period of rapid filling.
In the latter half of this period, there is no clear velocity
component in the free wall of the RV in Fig. 2(c-1) nor in
the posterior wall of the LV in Fig. 2(c-3). There are some

3408

Jpn. J. Appl. Phys. Vol. 38 (1999) Pt. 1, No. 5Bvibration components with a frequency of about 10 Hz in the
IVS of Fig. 2(c-2).
Also, there are no remarkable differences between the velocity signals, that is, all points in the three walls move inparallel. Thus, in the latter half of the period, the wall is grayin Fig. 2(d-2).
4. Measurement for a Patient with Dilated-cardiomyopathy
4.1 In vivo experiments and results
As an example of noninvasive diagnosis of the myocardium, we applied the proposed method to the IVS of a 57year-old male patient with dilated-cardiomyopathy (DCM).
The M-mode image, the ECG, the waveforms of the velocity signals, the normalized speed of change in thickness, Si (t),and the B-mode image of the IVS are respectively shown in
Figs. 3(a), 3(b), 3(d), 3(e), and 3(f). In this measurement,
the inner pressure of the LV is simultaneously and invasively
measured with catheterization, as shown in Fig. 3(c). Fromthe inner pressure, the boundaries among the six periods described above are largely confirmed.
4.2 Comparison of normal subject with patient
For the healthy subject, the thickness of the IVS is about
10 mm, while for the patient with DCM, the IVS is about
20 mm.
By comparing the velocity signals in Fig. 3(d) with thosein Fig. 2(d-2), the envelopes of the waveforms can be seen tobe similar.
Comparison of the normalized speed of change in thickness
in Fig. 3(e) with that in Fig. 2(d-2) shows that the change inthickness is not homogeneous for the patient. The reason isthat the myocardial fibers have complex directions, especiallyin the half of the IVS next to the RV.
Especially in the period of slow filling, the gray components are not clearly recognized, that is, the myocardium always moves to become thick or thin, even in the diastole.

H. K ANAI et al.

5. Conclusions
In this paper, we have applied the method developed to thefree wall of the RV, the IVS, and the posterior wall of the
LV of a healthy young male volunteer and the IVS of a malepatient with DCM. From the relationship among the results
for the three heart walls and the differences between the subjects, the velocity waveforms and the changes in thickness
have been characterized for each period during one cardiac
cycle.
In our previous study, detected velocity signals were analyzed in the frequency domain only for the period around thesecond heart sound emission. The analysis will next be applied to the velocity signals for each of six cardiac periods
based on the results presented in this paper.
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 also being conducted.
Acknowledgements
The authors are grateful to Professor Emeritus Noriyoshi
Chubachi of Tohoku University, Professor Kunio Shiratoof Tohoku University School of Medicine, and Dr. Yoshiro
Uzuka of the Sendai Center for Hematologic Disorders fordiscussions and encouragement, and Dr. Eiichi Kamata of Tohoku University School of Medicine for helpful discussion
and assistance with experiments.

1) H. Kanai, H. Hasegawa, N. Chubachi, Y. Koiwa and M. Tanaka: IEEE
Trans. Ultrason. Ferroelectr. & Freq. Control 44 (1997) 752.
2) H. Kanai, M. Sato, Y. Koiwa and N. Chubachi: IEEE Trans. Ultrason.
Ferroelectr. & Freq. Control 43 (1996) 791.
3) C. Kasai, K. Namekawa, A. Koyama and R. Omoto: IEEE Trans. Sonics& Ultrason. 32 (1985) 458.
4) A. P. G. Hoeks, C. J. Ruissen, P. Hick and R. S. Reneman: UltrasoundMed. & Biol. 11 (1985) 51.
5) D. E. Hokanson, D. J. Monzersky, S. D. Sumner and D. E. Strandness,
Jr.: J. Appl. Physiol. 32 (1972) 728.