REGULAR PAPER

Japanese Journal of Applied Physics 53, 07KF25 (2014)
http://dx.doi.org/10.7567/JJAP.53.07KF25

Ultrasonic visualization of propagation of myocardial vibration driven
by electrical excitation of myocardium of rat in ex vivo experiment
Yuta Fujita1, Hideaki Tagashira2, Hideyuki Hasegawa1,3, Kohji Fukunaga2, and Hiroshi Kanai3,1*
1

Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan
Graduate School of Pharmaceutical Sciences, Tohoku University, Sendai 980-0845, Japan
3
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
E-mail: kanai@ecei.tohoku.ac.jp
2

Received November 29, 2013; accepted April 21, 2014; published online June 26, 2014
For the realization of noninvasive and regional myocardial tissue characterization, in the present study, we attempted to elucidate thecharacteristics of the myocardial response to electrical excitation and its propagation by an ex vivo experiment using a rat left ventricular wall. To
visualize such a propagation phenomenon, whose speed is up to several m/s, high-frame-rate ultrasound was used to measure the myocardial
vibrations driven by electrical excitation at 72 points along the heart wall with 200 µm intervals at a frame rate of 3472 Hz. The propagation of
myocardial vibration was visualized by estimating the delay time between vibration waveforms measured in the reference ultrasonic beam andeach ultrasonic beam using the cross-correlation function between the vibration waveforms. From the estimated delay time, we visualized the
propagation of myocardial vibration caused by electrical excitation. The propagation speed was estimated to be 2.5 m/s in the entire excised
myocardium. It was also estimated to be 1.8 m/s in the middle of the heart wall and 2.2 m/s at the internal and external surfaces of the leftventricular wall. The results showed that the myocardial vibration driven by electrical excitation could be measured with high-frame-rate ultrasound.
© 2014 The Japan Society of Applied Physics

1.

Introduction

About 7.3 million people in the world and 20 thousandpeople in Japan die of heart diseases in a year.1,2) Serious
heart diseases require a long-term advanced care andenormous costs for treatment. For example, the cost for
health care in Japan was 742 million yen in 2011.3)
Therefore, the selection of an appropriate treatment and theprevention of the onset of such diseases are essential. To that
end, there is a need for developing accurate diagnostic
methods that can be applied repeatedly to monitor thecondition of a patient.
Electrocardiography,4) chest X-ray, computed tomography(CT),5) magnetic resonance imaging (MRI),6,7) and ultrasound8) are commonly used for the diagnosis of heartdiseases. Electrocardiography is an invaluable clinical tool
for the diagnosis of cardiac failure. Chest X-ray can be used
to diagnose pathological conditions, but further diagnosis,
such as an invasive catheterization, must be performed if
the required information cannot be obtained. CT and MRI
enable morphological diagnosis from three-dimensional
images and the evaluation of coronary artery stenosis with
contrast agents. Although conventional ultrasonography
enables morphological diagnosis, it is also used for theevaluation of heart wall motion9–11) and myocardial tissue
characterization.12,13) It is very useful because abnormal wallmotion occurs frequently in cases of heart diseases. Also,
myocardial tissue changes due to heart diseases. However, a
new method is necessary for the identiﬁcation of the diseased
region, such as the regional infarcted area in the heart wall,
for the accurate diagnosis of heart diseases.
Our study group previously examined the rapid responseof the excised myocardium of a rat driven by electricalexcitation (change in thickness of 30 µm and vibration
velocity of 0.5 mm/s).14) From our ﬁndings, we measured
the propagation of vibration in the interventricular septum
at about 10,000 points caused by the conduction of theelectrical excitation15) in vivo. Furthermore, we showed
possibilities of the ultrasonic measurement of the propagationof myocardial contraction in response to the electricalexcitation in vivo.16)
In our previous ex vivo experiments using an excised
myocardium of a rat, the propagation of myocardial vibration
driven by electrical excitation was not identiﬁed because the
myocardial vibration was measured at only one point on
the myocardial tissue using laser velocimetry. Therefore, thecausality among the electrical excitation, myocardial vibration, and its propagation is still unclear. Therefore, in thepresent study, we measured the myocardial contraction
response driven by electrical excitation ex vivo at hightemporal and spatial resolutions using ultrasound. Electricalexcitation propagates at a velocity of several m/s.17–20)
Therefore, in the present study, myocardial vibrations were
measured at a high temporal resolution of 3472 Hz with highframe-rate ultrasound.
2.

Materials and methods

2.1

Experimental setup
Figure 1 shows a schematic diagram of the experimental
system used to measure the propagation of myocardial
vibration driven by electrical excitation. The specimen used
was the left ventricular wall excised from the heart of a
Sprague-Dawley rat (11 weeks old, 368.1 g). The size ofthe myocardium was 5.1 © 15.4 mm2. The myocardium was
ﬁxed by hooks attached to an XY stage and a force transducer(Fig. 2). The force transducer was employed to measure thetension T(t) along the longitudinal axis of the myocardium
generated by myocardial contraction. The myocardium wasstimulated from the apical side by an electrical stimulator
as in the propagation of the electrical excitation in vivo. In
addition, the ventricular cavity side of the myocardium wasplaced near the ultrasonic probe. The water tank was ﬁlledwith Krebs-Henseleit solution, which was warmed at 37 °C,
and 95% O2 gas was richly melted into the solution. The
size of the tank was 100 © 100 © 100 mm3. The absorbing
material was placed at the bottom of the water tank in orderto reduce the effect of reﬂected ultrasonic waves. The
myocardium was electrically stimulated by a rectangular

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Jpn. J. Appl. Phys. 53, 07KF25 (2014)

Y. Fujita et al.

oscilloscope

attenuator

electric
stimulator

force
transducer
ultrasonicequipment

XYZ stage

thermometer

ultrasonic probebase of heart

myocardium
XY stage

cardiac apex
0, 1, 2,...,

Krebs−Henseleit
solution

70, 71beam number
acoustic−absorption material

Fig. 1. (Color online) Experimental setup for measuring the vibration of the myocardium extracted from the excised rat heart.

ultrasonic probe
0.2 mmvibration
direction

propagation of vibration
caused by contraction++
myocardium

beam number n = 0, 1, 2, ..., 70, 71
Fig. 3. (Color online) Illustration of measurement of minute vibration
velocity waveforms. Spacings of ultrasonic RF data were 0.2 mm and 20 µm
in the axial and lateral directions, respectively.

Fig. 2. (Color online) Myocardium ﬁxed by two hooks.

pulse e(t) at a repetition frequency of 2 Hz at 4 V. Platinum
electrodes were attached to an XYZ stage for the adjustmentof the geometry. By adjusting the voltage and the distanceof the edge of the myocardium from the electrodes, only
a very small part of the myocardium at the edge could
be activated by electrical excitation, and the subsequent
propagation of the myocardial contraction to the other side of
the myocardium could be observed. Electrodes were coatedwith plastic paste other than their tips in order to prevent theformation of extra electric ﬁelds in the solution. The distance
between the myocardium and the electrodes was about
1.0 mm. The pulse waveform was also input to the ultrasoundsystem for data acquisition. The acquisition of ultrasonic data
was triggered by electrical stimulation.
2.2

Acquisition of ultrasonic data
The vibration velocity v(t) caused by myocardial contraction
in response to electrical excitation was measured by ultrasound. Figure 3 illustrates the propagation of the myocardial
contraction response.
To measure myocardial vibrations at a high temporal
resolution, parallel beam forming (PBF)21,22) was performed

with ultrasonic diagnostic equipment (Hitachi-Aloka
ProSound ¡-10) equipped with a 10 MHz linear array probe.
In this method, the number of transmissions was reduced
using plane waves in transmission and creating multiple
focused receiving beams per transmission. In the present
study, the number of transmissions was 3, and 72 receiving
beams were obtained by 3 transmissions. As a result, a highframe rate (1/¦T; ¦T: frame interval) of 3472 Hz was
realized. The sampling frequency of the beamformed RF
signal was 40 MHz. Figure 4 shows a B-mode image of the
myocardium.
Vibration velocities were estimated along 72 beams (beamnumber M = 0, 1, + , 71) with intervals of 0.2 mm. Alongeach beam, vibration velocities were estimated at intervals of
20 µm in the axial direction. In the present study, the minutevibration velocity v(t) caused by myocardial contraction wasmeasured by the phased-tracking method.23) The phasedtracking method has been used for determining cardiovascular dynamics24,25) and also for obtaining morphologicalinformation.26,27) The average velocity v(t + ¦T/2) of an
object at the frame interval ¦T is accurately estimated using
the phase shift between the received ultrasonic pulses as

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Jpn. J. Appl. Phys. 53, 07KF25 (2014)

2.3 Visualization of distribution of propagation timedelays of vibrations

14.4 mm

In the present study, the propagation of myocardial vibration
was visualized by estimating its delay time. The propagation
delay time was deﬁned as the delay time of the vibration
velocity vj,i(n) measured in each (i-th) ultrasonic beam fromthat measured in the reference beam. The distributions ofpropagation delays were obtained along three manuallyassigned lines (lines A, B, and C in Fig. 4) at different depthsj ( j = 0, 1, and 2). To consider the difference in ﬁber
direction between the inside and surface of the myocardium,propagation speeds were measured on 3 lines. Lines A and C
were selected to measure the propagation speed at the surfaceof the myocardium, and line B was selected to measure thepropagation speed inside the myocardium.
The delay time was estimated using the cross-correlation
function29) between the vibration velocities vj,Ref (n) and
vj,i (n) (n: frame number) in the reference and each beams.
The cross-correlation function rj,i (m) is expressed as
N1
X
1ðvj;Ref ðnÞ  v j;Ref Þ
rj;i ðmÞ ¼
j;Ref j;i N n¼0

19.6 mmabout 1.0 mm

Y. Fujita et al.

Power Spectrum [dB]Fig. 4. (Color online) Cross-sectional view of the myocardium andmanually assigned lines for analysis.

0
−10
−20
−30
−40
−50
−60
−70
−80
−90

0

300

600
900
Frequency [Hz]

1200

1500

 ðvj;i ðn þ mÞ  v j;i Þ;ð2Þwhere ·j,Ref and ·j,i are the standard deviations of vj,Ref (n) and
vj,i (n) for N frames, respectively. Moreover, v j;Ref and v j;i
are averages of vj,Ref (n) and vj,i (n) for N frames, respectively.
The delay time ¸j,i values were determined from the lag
mmax, which maximizes the cross-correlation function, as
mmax 0 ¦T.
To estimate the propagation speed of myocardial vibration,
the estimated delay time ¸j,i values were plotted as a functionof beam position i 0 ¦x (¦x: interval of beams). Then, thelinear regression line was determined by the least-squares
method.30) The propagation speed cs was estimated by the
inverse of the slope of the determined regression line. By
repeating the same procedure for other depths j, propagation
speeds cs at different depths j were estimated.
3.

Fig. 5. (Color online) Frequency components of the vibration velocity
waveform by myocardium contraction.

Tðx; tÞ
;
v tþ
¼ c0
2
4f0 T

ð1Þ

where c0 is the velocity of ultrasound, f0 is the center
frequency, and ðx; tÞ is the phase shift of the received
ultrasound signal during ¦T.
A low-pass ﬁlter with a cutoff frequency of 700 Hz wasapplied to the estimated vibration velocity v(t) to reduce thehigh-frequency noise. The cutoff frequency of 700 Hz was
selected so as not to remove velocity components due tomyocardial contraction (from 0 to 150 Hz)23) (Fig. 5). Also,a low-pass ﬁlter with a cutoff frequency of about 35 Hz
was applied to the measured tension T(t) to reduce electricalnoise. Furthermore, for the conﬁrmation of myocardial
contraction, the change in the thickness of the myocardium
was also estimated by the temporal integration of thedifference between velocities at the near and far surfaces ofthe myocardium.28)

In vitro experimental results

Figure 4 shows a B-mode image of the myocardium
measured in the present study. There are electrodes near the
0th ultrasonic beam that corresponds to the left edge of the Bmode. Vibration velocities v(t) were estimated along lines A–
C.
Figure 6 shows the measured myocardial contraction
response driven by electrical excitation. Figure 6(b) shows
the vibration velocities v0,32(t); v2,32(t), and the amplitude ofv2,32(t) is smaller than that of v0,32(t). The myocardial
contraction was triggered by the electrical stimulation signale(t) shown in Fig. 6(a). The change in the thickness of the^ was obtained as shown in Fig. 6(c) by the
myocardium hðtÞtemporal integration of the difference between v0,32(t) andv2,32(t). The tension T(t) measured by the force transducer
was also obtained as shown in Fig. 6(d). Unfortunately, thegenerated force was very small, and the signal-to-noise ratioof the tension waveform was very low. However, it can beobserved that the tension was generated by electricalstimulation. These results show that myocardial contraction
was caused by electrical excitation.
Figure 7 shows the vibration velocities v0–v71 measured ineach line. Around the 0th and 71st beams, amplitudes of

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Y. Fujita et al.

(a)Vibration Velocity [mm/s]

−5

(b)

Beam 32(line A)

−4
−3
−2
−1
0

contraction

relaxation

1
2

(c)

duration of contraction−relaxation

0

0.1

0.2
Time [s]0.3

0.4

Fig. 8. (Color online) Vibration velocity v32(t) in line A in Fig. 4 andillustration of durations of contraction–relaxation, contraction, andrelaxation.

(d)Fig. 6. (Color online) (a) Electrical stimulation pulses e(t) at a repetition
frequency of 2 Hz. (b) Measured vibration velocities v0,32(t) and v1,32(t) in^ of thelines A and C in Fig. 4, respectively. (c) Change in thickness hðtÞmyocardium estimated from (b). (d) Output T(t) of the force transducer.

(a)

(b)

(c)

Fig. 7. (Color online) Visualization of vibration velocities v0–v71 alongeach line.

vibration velocities are smaller than those around the central
beam because there were hooks near the 0th and 71st beams.
From the waveforms of the measured vibration velocities,
the durations of contraction and subsequent relaxation,
contraction only, and relaxation only were manuallyestimated as illustrated in Fig. 8. The estimated durations
were obtained as the averages for three contraction–
relaxation cycles with respect to line A in each beam (from30th to 40th beams). The vibration velocities v30(t)–v40(t)were analyzed because the ﬁxation by the hooks hardly had
any effect. The average durations of contraction–relaxation,
contraction, and relaxation were estimated to be 242, 74, and
168 ms, respectively.
Figures 9(a)–9(c) show the cross-sectional B-mode imageof the myocardium, the delay time distribution of myocardial
vibrations, and the average delay time plotted as a functionof distance from the reference point, respectively. The delay
time of the myocardial vibration at each spatial point wascalculated as the delay time from the myocardial vibration
at the reference point (4th ultrasonic beam position). The
reference point was closer to the stimulation electrode, andthe delay time increased when the distance from the reference
point (beam 4) increased, as shown in Fig. 9(c). By
estimating the regression line using the least-squares method,
the propagation speed cs was estimated to be 2.5 m/s.
For a more detailed analysis of propagation of contraction,
we examined the regional propagation of contraction inside
and at the surface of the myocardium. Figure 10 shows thedelay time distributions of vibration velocities obtained alonglines A, B, and C. Vibration velocities were estimated atadditional spatial points in the region with a width of 300 µm
in depth from each line. In Fig. 10, the reference beam was
the 4th beam (beam number m = 4). As can be seen in
Fig. 10, although slight variations exist, the estimated delay
times were similar in the 300 µm regions from the respectivelines (A, B, and C) in the same ultrasonic beam. Therefore,
the delay time at each ultrasonic beam was obtained byaveraging the delay times in the 300 µm region along thecorresponding beam around the line of interest (A or B or C)
for a stable estimation of the propagation speed of theelectrical excitation. Figure 11 shows the average delay
times plotted as a function of the distance from the reference
beam (m = 4) obtained with respect to lines A, B, and C.

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Jpn. J. Appl. Phys. 53, 07KF25 (2014)

0.96
mm

beam 4
reference point(a)beam 61

Depth from line A [µm](a)Y. Fujita et al.

0

100
200

(b)
0.96
mm

beam 4

beam 61300

Delay time[ms]0

Depth from line B [µm]

(b)

(c)

Delay time [ms]
10
9
8
7
6
5
4
3
2
1
0
2
4
6
8
10
12
Distance from beam 4 [mm]Delay time [ms]
12

0

10
100

8
6

200

4
2

300

0
0

Depth from line C [µm]

(c)
0

100
200

[mm]

300

Fig. 9. (Color online) (a) Cross-sectional view of the myocardium.
(b) Delay time distribution of myocardial vibrations. (c) Average delay times
plotted as a function of distance from the reference point.

By estimating the regression line using the least-squares
method, the propagation speed cs was estimated to be 1.8 m/s(line A), 2.2 m/s (line B), and 2.2 m/s (line C).
Furthermore, the time of the beginning of contraction tc
from the electrical stimulation was also estimated using theestimated propagation speed of the electrical excitation.
The propagation velocity cs along line A was used because
the correlation between the measured delay time and theregression line was highest (R2 = 0.8735). To obtain the timeof the beginning of contraction tc, the time at the risingedge of the vibration velocity measured in the 4th beam was
manually identiﬁed to be 19.6 ms. Then, the time required
for the electrical excitation to propagate from the edge ofthe myocardium to the 4th beam was estimated to be 0.87 ms
by dividing the distance (3.4 mm) from the edge of the
myocardium to the 4th beam by the propagation velocity cs
of 2.5 m/s. Finally, the time of the beginning of contraction
tc was estimated to be (19.6 ms) ¹ (1.34 ms) = 18.3 ms byassuming that the propagation delay of the electric ﬁeld to
propagate from the electrode to the edge of the myocardium
was negligible (propagation speed was that of light in water).
4.

Discussion

In the present ex vivo experiment, after setting the voltage ofthe electrical stimulation pulse, the electrodes were put closer
to the myocardium. This movement of the electrodes was

0

2
4
6
8
10
Distance from beam 4 [mm]12

Delay time [ms]
10
9
8
7
6
5
4
3
2
1
0
2
4
6
8
10
12
Distance from beam 4 [mm]Fig. 10. (Color online) Delay time distributions of myocardial vibrationsin the regions of 300 µm from lines A (a), B (b), and C (c).

stopped when the myocardium just began to contract. By thisprocedure, only the edge of the myocardium was stimulatedby the electrical stimulation pulse, and we could avoid thestimulation of the entire myocardium at the same time.
However, the electrical voltage at each part of the
myocardium could not be measured in the present study,
and the distribution of the electrical ﬁeld in the myocardium
is expected to be measured in our future work.
In Fig. 6, the input signal for electrical stimulation e(t) wasa rectangular pulse. However, the actual measured waveform
became a gradually descending waveform because Krebs–
Henseleit solution contained a large amount of electrolyte.
There is no effect on contraction because this phenomenon
also occurs in the ventricular muscle in vivo.31) In addition,
the measured tension T(t) was affected by electrical noise.
We need to modify the experimental system to measure thetension waveform with much better signal-to-noise ratio. In
our previous study, we measured the contractional characteristics using papillary muscle.14) The tension T(t) measured
previously was 0.5 mN (100 times larger) and the previously^
measured change in thickness hðtÞwas similar to thatmeasured in the present study. This is because electrodes
were placed parallel against the papillary muscle and the07KF25-5© 2014 The Japan Society of Applied Physics

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Y. Fujita et al.

(a)larger than that of line A, ultrasonic echoes could be obtainedwith a better signal-to-noise ratio in line C than in line B.
However, there are distinct peaks in Fig. 11(c) at distancesfrom the 4th beam of 2, 4, and 6 mm. There are coronary
arteries on the external surface of the myocardium (corresponding to line C), and coronary arteries might affect the
propagation phenomenon.
It is known that the conduction speed of the electrically
excited wave along the human ventricular muscle is about
0.3–1.0 m/s.32) In the present study, however, the propagation
speed of myocardial vibration cs driven by electricalexcitation was estimated to be 1.8–2.5 m/s, corresponding
to the conduction speed in Purkinje ﬁbers. The speciﬁc
resistance of a Purkinje ﬁber is smaller than that of aventricular muscle in a mammalian heart.33,34) Therefore, theelectrical excitation might not only propagate through aventricular muscle but also through a Purkinje ﬁber. Such a
propagation speed of 4 m/s was also found in the propagationfrom the base side of the intraventricular septum (IVS) to theapical side in the previous study.15,32)
The beginning of contraction tc was delayed from theelectrical stimulation pulse by 18.3 ms. To generate themechanical response (myocardium contraction), Na+ andCa2+ were introduced into cells by the opening of Na+ andCa2+ channels by action potential induced by electricalstimulation. This phenomenon leads to the slipping movement of myosin ﬁlaments, resulting in the deformation of
myoﬁbrils as a trigger of Ca2+ inﬂow. The delay time of
18.3 ms was considered to be caused by the above responseto the electrical stimulation.35,36)

(b)

(c)

5.

Fig. 11. (Color online) Average delay time plotted as a function of
distance from the reference beam (4th beam). The regression lines were
determined by the least squares-method. (a) Line A. (b) Line B. (c) Line C.

papillary muscle was stimulated by an electrical pulse with anamplitude that was 2.5 times larger than that in the present
study. On the other hand, the times of the beginning ofcontraction tc after the electrical stimulations were very
similar (about 19.0 ms) in the two studies.
In Fig. 9(b), the points with low brightnesses, whose
acoustic impedance is supposed to be low, show slow
contraction responses. Therefore, elastic moduli of thesepoints would be small, and small elastic moduli might lead toslow contraction responses.
In Fig. 11, the correlation coefﬁcients R2 in (b) and (c)2(R = 0.3 and 0.7, respectively) were lower than that in (a)(R2 = 0.8). Along line B, myocardial vibration velocities
were not obtained with good signal-to-noise ratios because
the amplitudes of ultrasonic echoes from the inside of the
myocardium were small. Although the depth of line C is

Conclusions

In the present study, we performed the ex vivo measurementof the characteristics of the myocardial response to theelectrical excitation and the propagation of myocardial
vibration in an excised left ventricular myocardium of a rat
with high-frame-rate ultrasound. Results indicate that thecontractional response occurred about 18.3 ms after theelectrical stimulation, followed by a change in thickness,and that a tension of about 5 µN occurred 10.0 ms later. The
vibration velocity of the myocardium was estimated to beabout 4 mm/s during contraction and about 2 mm/s during
relaxation. Durations of contraction–relaxation, contraction
only, and relaxation only were also estimated to be 242, 74,
and 168 ms, respectively. Furthermore, we visualized the
propagation of myocardial vibration, and the propagation
speed cs was estimated to be 1.8–2.5 m/s. From these results,
we showed that the propagation of the myocardial contraction
response driven by electrical excitation can be measured withultrasound, and that the visualization of the propagation of
myocardial contraction can be useful for the tissue characterization of the regional heart muscle.

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