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Local two-dimensional distribution of propagation speed of myocardial
contraction for ultrasonic visualization of contraction propagation
To cite this article: Akane Hayashi et al 2019 Jpn. J. Appl. Phys. 58 SGGE05

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REGULAR PAPER

Japanese Journal of Applied Physics 58, SGGE05 (2019)https://doi.org/10.7567/1347-4065/ab0d0bLocal two-dimensional distribution of propagation speed of myocardial
contraction for ultrasonic visualization of contraction propagation
Akane Hayashi1, Shohei Mori2 , Mototaka Arakawa1,2* , and Hiroshi Kanai2,1
1

Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan2*

E-mail: arakawa@ecei.tohoku.ac.jp

Received November 9, 2018; accepted January 15, 2019; published online June 11, 2019
The propagation of myocardial contraction caused by the conduction of electrical excitation in the heart has been visualized in our previous study.
However, it was assumed that the contraction propagated parallel to the heart wall and the propagation speed was constant within themeasurement area. In the present study, we estimated the two-dimensional propagation speed of contraction at each local area by ultrasonicmeasurement, and examined the mechanism of the contraction propagation in the heart by calculating the spatial distribution of the propagation
speed vectors. By applying the proposed method to the interventricular septum of the human heart, the propagation speed in the lateral direction
was approximately 1.6 times faster than that in the beam direction. The significant difference in propagation speeds between the specialized andordinary myocardia was detected successfully. This study suggests that the proposed method can detect the myocardial ischemic and arrhythmia
regions non-invasively. © 2019 The Japan Society of Applied Physics

1. Introduction

Approximately 9.4 million people worldwide die annuallyowing to heart diseases, and the number of deaths has been
increasing.1) Heart disease ranks top in the cause of death andconstitutes 17% of all-cause mortality. Therefore, the prevention of the onset of heart diseases and their appropriate
treatments are essential, and the development of a diagnostic
method that can be applied repeatedly with high accuracy isrequired urgently. Conventionally, chest X-ray,2) computed
tomography,3) magnetic resonance imaging,4,5) and medical
ultrasound are typically used for the diagnosis of heartdiseases. Ultrasonic diagnosis using medical ultrasound ishighly useful because it is non-invasive in vivo, the equipment is comparatively inexpensive, and the minute movements and temporal changes of organs and blood vessels canbe captured repeatedly in real time.6–13)
The representative heart disease is an ischemic heartdisease, and the important condition is myocardial infarction.
The lesion where myocardial infarction occurs is known as
the ischemic region, injured region, and infarct region in theorder of disease progression.14) The ischemic region is theregion where the coronary narrows and the blood does notreach the myocardium. Fatal necrosis of the myocardium canbe avoided by prompt re-perfusion in the ischemic region. In
the next stage, i.e., the injured region, it is barely possible to
avoid myocardium necrosis. However, recovery cannot be
expected in the infarct region in which the myocardium is
necrotic when the coronary narrows further and becomesblocked. Therefore, the non-invasive and rapid identiﬁcationof the myocardial ischemic region is crucial for the diagnosis
and subsequent appropriate treatments in the early stages ofischemic heart diseases.
To detect and identify the myocardial ischemic regions, itis necessary to ﬁrst clarify the characteristics of myocardium
in the normal condition. Detection of the myocardial contraction response caused by the conduction of electricalexcitation in the heart has been studied, and the excitation
process and myocardium contraction caused by the excitation
have been conﬁrmed.15–19) We ultrasonically detected thepulsed minute vibration (displacement amplitude: 30 μm,

velocity amplitude: 0.5 m s−1) that occurred with the myocardial contraction at 15 ms after delivering an electricalstimulus in the papillary muscle extracted from an isolated rat
heart.20) We measured the pulsed vibrations at about 10 000
points in the interventricular septum (IVS) in the time of
conduction of the excitation at electrocardiographic QRS
waves and at the occurrence of the ﬁrst heart sound in thehuman heart, and conﬁrmed the propagation of myocardial
contraction.21,22) Moreover, we applied the ultrasonic measurement to both the IVS and left ventricular (LV) posteriorwall in the human heart simultaneously, and conﬁrmed the
propagation of myocardial contraction along the conduction
path of the electrical excitation.23)
Meanwhile, the detection and imaging of the myocardialischemic regions have been studied.24–29) The propagation
speed of the myocardial contraction response caused by theelectrical excitation decelerated to 0.7 m s−1 in the ischemic
region, whereas it was 1.2 m s−1 in the normal region in the
open-chest canine heart.30) We applied our ultrasonic method
to the IVS of open-chest swine hearts, and compared the
propagation speeds of myocardial contraction in the normal
and ischemic myocardia.31,32) The estimated propagation
speeds were 2.7 m s−1 in the normal myocardium and1.4 m s−1 in the ischemic myocardium, and we conﬁrmedthat the propagation speed of myocardial contraction decreased by approximately 50% owing to ischemia.
However, it was assumed that the myocardial contraction
propagated parallel to the heart wall and the propagation
speed was constant within the measurement range in ourprevious study. A more detailed visualization of the propagation of myocardial contraction is required to establish thediagnostic method for the detection of the myocardialischemic regions and demonstrate the propagation of contraction occurring in the heart physiologically. Although themethod of estimating the propagation speed vectors was
proposed in the past,33) electrical activation of the myocardium was measured by electrodes attached to the epicardia inswine hearts, and the propagation of myocardial contraction
was not measured non-invasively.
The propagation speed of myocardial contraction can be
estimated by measuring the minute movements caused by

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Fig. 1. (Color online) Transmission method of ultrasound. (a) Diverging wave and (b) focused wave.

contractions in the heart wall using ultrasound. The blockmatching method is used widely for measuring the
movement.34–36) In our previous study, the movement of theheart wall was measured by the block matching method, andthe velocities with minute vibrations at multiple points in the
myocardium were obtained.37,38) This method enables movements to be tracked by applying the cross-correlation method
to the speckle pattern within a region of interest (ROI) in
successive frames. Therefore, it was necessary to measure theRF signals with high-frame rates and to acquire them densely
in the lateral direction. The high-frame-rate measurement was
realized by transmitting diverging or plane ultrasound waves,
as shown in Fig. 1(a). The dense acquirement of the RF signals
in the lateral direction was realized by forming the received
beams densely. However, the amount of calculation increases
in this method, and sophisticated diagnostic equipment isrequired. In addition, because the valves and the walls movequickly in the heart, the S/N decreases in the measurement
using diverging or plane ultrasound waves. The measurement
using focused waves is desirable to obtain the velocity withminute vibrations accurately at multiple points in the heartwall.
We realized the high-frame-rate measurement by transmitting focused waves sparsely, as shown in Fig. 1(b). The
myocardial contraction response that is the movement of the
IVS to the apical side and to the LV side, was conﬁrmed at
the onset of ventricular contraction.39) In the present study,
we measured the movement of the IVS to the LV side, i.e.,the contraction response of the IVS in the beam direction on
the LV long-axis view at several thousands of points, andconﬁrmed that the measured contraction response propagatedin the lateral and beam directions at each local area. Further,
25 ms were required for the myocardial contraction to
propagate within the measurement range, assuming that the
propagation speed of contraction was 4 m s−1, which is theupper limit of the conduction speed of electrical excitation,40)
and the measurement range of the propagation direction was
100 mm. The contraction propagation can be captured
sufﬁciently by measuring using a frame rate of about
400 Hz. We estimated the two-dimensional propagation
speed of myocardial contraction at each local area by
ultrasonic measurement, and examined the mechanism of
the contraction propagation in the heart by calculating the
spatial distribution of the speed vectors. By increasing thenumber of subjects since the recent report,41) we improved
the reliability of the results, and discussed the results
physiologically, in detail.

2. Methods
2.1. Measurement of velocity with minute vibrationsin the myocardium

Because the focused waves were transmitted sparsely and theRF signals were not acquired densely in the lateral direction,
the velocities with minute vibrations in the myocardium wereobtained by applying the phased-tracking method.42,43) The
phase difference Dq (t; l ) of the received signals between thetimes t and t + DT at the center angular frequency w0 was
calculated, and the velocity v (t; l ) with minute vibrations at
each time t was obtained byv (t ; l ) =c0 Dq (t ; l)
,
2DT
w0

(1 )

where c0 is the velocity of ultrasound in soft biologicaltissues, DT is the transmission interval of the ultrasonicpulse, and l is the distance from the center of surface of theultrasound probe. The method stated above can be implemented with the current diagnostic equipment because only asmall amount of calculation is involved.
Velocity waveforms with minute vibrations in the myocardium were obtained as shown in Fig. 2 by the phased-tracking
method. Displacement waveforms obtained by integrating thevelocity waveforms are also shown. Although several studies
have reported the detection of myocardial contraction using
displacement waveforms,7,8,19,27,28,30,44–46) it is possible tomeasure not only the visible contraction but also minutevibrations caused by contraction using velocity waveforms.
The contraction response at the time of the electrocardiographic QR interval representing the onset of ventricular
contraction can be identiﬁed as the bimodal movements of
myocardium toward the LV, i.e., the bimodal positive waveform in velocity waveforms, although the displacement waveforms were almost smooth. The bimodality of the contraction
response has also been conﬁrmed in our previous study,31) andthe event was associated with the myocardium contraction. It
is possible to accurately detect the myocardial contraction
response by analyzing the velocity waveforms with minutevibrations in the myocardium. Therefore, the velocity waveforms are useful for estimation of the two-dimensional
propagation speed of myocardial contraction at each local area.
2.2. Delay time measurement of myocardial
contraction response23,32)
The velocity waveforms of the beam direction with minutevibrations were obtained simultaneously at several thousandsof points in the myocardium by the phased-tracking

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Fig. 2. (Color online) Electrocardiogram (ECG), phonocardiogram (PCG), velocity waveforms with minute vibrations and displacement waveforms ininterventricular septum.

method.42,43) The arrival time difference of the contraction
response was calculated using the velocity waveforms v (t; l0 )with minute vibrations at the reference position l0 and v (t; lij )at the position lij with the beam i and depth j from the probe.
The reference position l0 was set at the measurement position
where the amplitude of the velocity waveform was the
maximum in the correlation window among all the measured
velocity waveforms. The delay time tp of the contraction
response v (t; lij ) at each position lij from the contraction
response v (t; l0 ) at the reference position l0 was determinedby applying the cross-correlation method. The calculateddelay time tp from the reference waveform v (t; l0 ) wasconverted into the delay time tij [s] from the electrocardiographic R wave representing the onset of ventricular contraction. The differences in the delay time of the contraction
responses can be compared among multiple measurements byunifying the criteria for calculating the delay time.
In the electrocardiographic QR interval at the onset ofventricular contraction, the peak at which the myocardium
moved to the LV, i.e., the velocity with minute vibrations
became positive, was regarded as the contraction response,
and the center of correlation window was set at that time. The
width of the correlation window was set to be the same as thewidth of the contraction response waveform, and the searcharea, that is the range to move the correlation window was
limited to approximately 25 ms before and after the correlation window. The propagation time of myocardial contraction
within the measurement range was calculated as 25 ms
assuming that the propagation speed of contraction was
4 m s−1, which is the upper limit of the conduction speedof electrical excitation,40) and the measurement range of
propagation direction was 100 mm.
2.3. Propagation speed estimation of myocardial
contraction response
In Cartesian coordinates, the calculated delay time distribution {tij} of the myocardial contraction response was expressed as (x, y, txy ) by the measurement position (x, y) anddelay times {txy}. A quadratic surface T (x, y) was ﬁtted by
the weighted least-squares method in the ROI centered ateach measurement position (x 0 , y0), as shown in Fig. 3. The

surface T (x, y) was given by
T (x , y) = a + bx + cy + dx 2 + exy + fy 2 ,(2 )where a, b, c, d, e, and f are coefﬁcients. In the present study,
the size of the ROI for ﬁtting the quadratic surface T (x, y) was
7.7 mm in the beam direction and ﬁve beams in the lateral
direction. If the size of ROI is enlarged than the region that thequadratic surface can be ﬁtted to the delay time distribution,
the result becomes insufﬁcient to ﬁt the delay time distribution
because of the lack of the degree in the ﬁtting function, and theestimated result of T (x, y) becomes averaged. The delay time
distribution within a ROI is shown in Fig. 3, and it was judgedthat the quadratic surface can be appropriately ﬁtted. The ROI
along the delay time was not limited, and the correlation value
for the reference waveform in the calculation of the delay time
tp was used as the weight for ﬁtting T (x, y) in contrast to the
resent report.41) Then, the variability in the propagation speed
vectors was further reduced.
The two-dimensional propagation speed of myocardial
contraction was subsequently calculated using the gradientof the surface T (x, y). The gradient vector was expressed asT = [¶T /¶x, ¶T /¶y]T , and the propagation speedve (x 0 , y0) was estimated by⎡ dx ⎤ ⎡ Tx ⎤⎢ ⎥ ⎢ Tx2 + Ty2 ⎥⎢⎥ve (x 0, y0) = ⎢ dT ⎥ = ⎢
⎥,
T
dy
y
⎢ ⎥
⎢
⎢⎣ dT ⎥⎦ ⎢ T 2 + T 2 ⎥⎥
y ⎦
⎣ x

(3 )

where Tx = ¶T /¶x and Ty = ¶T /¶y.33,46)
Because the local and two-dimensional propagation speedof myocardial contraction was estimated although only theaverage speeds were estimated in our previous study,23,31,32)
the estimation of spatial distribution of the propagation speed
vectors became possible.
3. In vivo experiment3.1. Experiment environment

In vivo measurement was applied to the IVS of three healthy
males in their early 20 s using an ultrasound diagnostic

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Fig. 3. (Color online) Quadratic surface ﬁtting to delay time distribution {tij}.

equipment (SSD-6500, Aloka) with a sector probe of 5-MHz
center frequency. The transmission pulse repetition frequency
was 6510 Hz, and the high-frame-rate measurement of 434 Hz
was realized by reducing the number of beams to 15. The
sampling frequency was 20 MHz and the angle between
successive beams was 5.6°. The measurement interval in the
beam direction was 38.5 μm because the velocity c0 of
ultrasound in the soft biological tissue was assumed to be
1540 m s−1. Figure 4 shows the acquired B mode image and theacquisition area of the RF data. The beam in the basal side in
the heart was beam 0, and that in the apical side was beam 14.
The B mode image in Fig. 4(a) was acquired with the frame rateof 63 Hz and 103 beams to identify the position of the IVS.
3.2. Results
Figure 5 shows the delay time distribution {tij} of the
myocardial contraction response. The reference position l0
was set at approximately 33 mm in the depth from the probe
in beam 7. The delay time increased from the basal side
(beam 0) toward the apical side (beam 14), i.e., themyocardial contraction response propagated from the basal
to apical sides, as in our previous study.23)
Figure 6 shows the estimated result of the propagation
speed vectors {ve (x 0 , y0)}. The direction and magnitude of the
propagation speeds were indicated by the direction and colorof the arrows, respectively. The speed vector was indicatedevery 30 measurement positions in the beam direction. The
propagation speed was represented as the speed vector ineach ROI such that the local and two-dimensional estimationof the propagation speed became possible.

Figure 7 shows the result of decomposing the estimatedpropagation speed vector {ve (x 0 , y0)} to the lateral and beam
directions at each position. The propagation to the apical side
(beam 14) was deﬁned as positive in the lateral direction, andthe propagation to the LV side was deﬁned as positive in the
beam direction. Focusing on the propagation in the lateral
direction, the contraction propagated from the basal to apicalsides in beams 3–14. Meanwhile, focusing on the propagation in the beam direction, the contraction propagated fromthe LV to right ventricle (RV) sides in beams 4–14.
Moreover, the absolute values of the propagation speed
were averaged in beams 4–14 where the contraction propagation was conﬁrmed. They were approximately 1.1 m s−1 and
0.5 m s−1 in the lateral and beam directions, respectively. The
propagation speed in the lateral direction was faster than thatin the beam direction.
The data for other heartbeats of the same subject andmultiple heartbeats of two other subjects were analyzed
similarly. Similar results were obtained for the delay time
distribution {tij} and propagation speed vectors {ve (x 0 , y0)}.
Figure 8 shows the propagation speed in the lateral and beam
directions at each position in ﬁve heartbeats for threesubjects. The propagation speed in the lateral direction was
distinctively faster than that in the beam direction in all
subjects. The average propagation speeds in the lateral andbeam directions were 1.1 ± 0.3 m s−1 and 0.7 ± 0.3 m s−1,
respectively. The propagation speed in the lateral direction
was approximately 1.6 times faster than that in the beam
direction.

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Fig. 4. (Color online) (a) B mode image41) and (b) schematic diagram of measurement (IVS: interventricular septum, RV: right ventricle, LV: left ventricle,
LVPW: left ventricular posterior wall, LA: left atrium, AV: aortic valve, MV: mitral valve).

4. Discussion

Fig. 5. (Color online) Delay time distribution {tij} of myocardial contraction responses.

Fig. 6. (Color online) Propagation speed vectors {ve (x 0 , y0)} of myocardial
contraction.

In the human heart, electrical excitation occurs in thesinoatrial node near the right atrium, and its excitation
propagates through the specialized myocardium (conducting
system) such as the atrioventricular node, bundle of His,
bundle branch, and Purkinje ﬁber, as shown in Fig. 9.
The surrounding ordinary myocardium which constitutes
the walls in the atrium and the ventricle contracts by theelectrical excitation in the specialized myocardium, and theheart acts as a pump to bring blood to all parts of the body.
The propagation speeds of myocardial contraction in thebundle branch and Purkinje ﬁber inside the IVS werereported to be approximately 2–4 m s−1 from the basal toapical sides.40) Meanwhile, that in the ordinary myocardium
was reported to be approximately 0.3–1 m s−1.40,47)
In the lateral direction, the myocardial contraction propagated from the basal to apical sides in beams 3–14, as shownin Fig. 7(a). In beams 3–14, because the specialized
myocardium runs inside the IVS laterally,14,40,47) the propagation direction of contraction coincided with that of theelectrical excitation that causes the myocardial contraction.
Meanwhile, in the beam direction, the contraction propagatedfrom the LV to RV sides in beams 4–14, as shown in
Fig. 7(b). The right bundle branch (RBB) and left bundle
branch (LBB) are the specialized myocardia in the RV andLV sides, respectively, on the surface of the IVS. Eachbundle branch is connected to each Purkinje ﬁber. The RBB
appears as a multiﬁlament with 1–2 mm in diameter in the
RV side on the surface of the IVS, whereas the LBB spreads
like a fan widely in the LV side.14,48,49) The RBB is difﬁcult
to be included in the ultrasonic measurement surface,whereas the LBB is easily included in it. When the RBB is
not captured and only the LBB is captured by measurement,
the propagation of contraction from the LBB is mainly
measured, then the propagation from the LV to RV sides isobserved. Therefore, it appears that the contraction propagation from the LBB and Purkinje ﬁber having a large
distribution range was measured dominantly in the beam
direction. Additionally, the presence of the specialized

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Fig. 7. (Color online) Propagation speeds of myocardial contraction in (a) lateral direction (positive: apical side) and (b) beam direction (positive: LV side).

Fig. 8. (Color online) Average propagation speeds of myocardial contraction in (a) lateral direction and (b) beam direction in multiple heartbeats(●: subject A, ▲: subject B, ■: subject C).

Fig. 9. (Color online) Schematic view of conduction of electrical excitationin human heart.

myocardium was indicated by the propagation speed in thelateral direction in beam 3. The propagation speed in the
beam direction indicated the propagation from the RV to LV
sides in beam 3 contrary to the propagation direction inbeams 4–14. The vectors in the lower left direction can besimilarly observed in beam 3 in Fig. 6. This is certainly
because the position where the specialized myocardium
entered into the IVS from the RV side was near beam 3, asshown in Fig. 9. Because the specialized myocardium enteredinto the IVS with lower left direction to the beam direction,
the contraction propagation of the positive component wasmeasured in the lateral and beam directions, respectively.
The estimated direction of propagation in the beam
direction varied signiﬁcantly than that in the lateral direction.
This is certainly because the estimation range of propagation
speed was approximately 20 mm, corresponding to ﬁvebeams in the lateral direction and 7.7 mm corresponding to
200 measurement points in the beam direction, and the range
was insufﬁcient to estimate the propagation speed in the

beam direction accurately. Because the IVS thickness isapproximately 7–12 mm, it is difﬁcult to further expand theestimation range in the beam direction. Further investigations
would be required to estimate the propagation speed ofcontraction in the beam direction accurately.
Moreover, the propagation speeds in the lateral and beam
directions were 1.1 ± 0.3 m s−1 and 0.7 ± 0.3 m s−1, respectively, and the propagation speed in the lateral direction wasapproximately 1.6 times faster than that in the beam direction. As mentioned above, the propagation speed of thespecialized myocardium is reported to be faster than that of
the ordinary myocardium.40,47) The contraction propagationin the lateral direction was affected by the specialized
myocardium that runs laterally, whereas the contraction
propagation in the beam direction reﬂected that in theordinary myocardium. Therefore, the result indicates thatthe propagation speed in the lateral direction is faster thanthat in the beam direction.

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In the present study, the quadratic surface T (x, y) was
ﬁtted to the delay time distribution within the ROI(7.7 mm × 5 beams) at each measurement position (x 0 , y0).
However, the further investigation about the size of the ROI
and the ﬁtting function are still needed. The appropriate
ﬁtting conditions could be proposed by changing the conditions and evaluating variability in the results among multiple
heartbeats of the same subject under each condition.
5. Conclusion

In the present study, we estimated the local and twodimensional propagation speeds of myocardial contraction,and examined the mechanism of the contraction propagationin the heart by calculating the spatial distribution of the speed
vectors. The spatial distribution of the propagation speed
vectors of myocardial contraction was estimated, and thecontraction propagation in the IVS was visualized in detailcompared to the conventional method. Moreover, the propagation speeds in the lateral and beam directions were
estimated as 1.1 and 0.7 m s−1, respectively. The signiﬁcantdifference in propagation speeds between the specialized
myocardium and ordinary myocardium were detected successfully.
The propagation of myocardial contraction reﬂected that ofelectrical excitation. Therefore, if the propagation of myocardial contraction could be visualized in detail by the
proposed method, the identiﬁcation of the myocardialischemia region, and the detection of arrhythmia could be
expected. In addition to the abnormality of the conducting
system, the propagation of myocardial contraction when theabnormality occurred could also be visualized.
ORCID iDs

Shohei Mori https://orcid.org/0000-0002-5494-1055
Mototaka Arakawa
https://orcid.org/0000-0001-9386645X
Hiroshi Kanai https://orcid.org/0000-0002-6567-1687

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