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Measurement of propagation of local and minute contractile response inlayered myocardium
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REGULAR PAPER

Japanese Journal of Applied Physics 60, SDDE02 (2021)
https://doi.org/10.35848/1347-4065/abeabf

Measurement of propagation of local and minute contractile response in layered
myocardium
Yu Obara1, 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: mori@ecei.tohoku.ac.jp

Received November 30, 2020; revised January 19, 2021; accepted March 1, 2021; published online March 25, 2021
The in vivo measurement of the contractile response caused by electrical excitation has been studied to detect myocardial ischemia in its earlystages. In the present study, we used our previously proposed local velocity estimator to measure the two-dimensional distribution of the strain rateusing high-density beam scanning to obtain propagation of the local and minute contractile response in the heart walls of healthy humans.
Alternate layers of contraction and relaxation were observed around the time phase representing the onset of the conduction of electricalexcitation. The contraction propagated along the direction of the myocardial fiber in the myocardial layer. These results indicated that the electricalexcitation conducted in each myocardial layer and the transmural shearing deformation occurred at the boundary between alternate layers ofcontraction and relaxation. The measurement of the propagation of the local and minute contractile response can reveal the effective contraction
with the transmural shearing deformation. © 2021 The Japan Society of Applied Physics

1. Introduction

The early detection of myocardial ischemia helps prevent theonset of fatal ischemic events, such as myocardial infarction.
Myocardial ischemia occurs in the endocardial region of theheart wall and progresses transmurally toward the epicardial
region.1–3) Thus, local measurement in the transmural direction of the heart wall has the potential to detect myocardialischemia in its very early stages and assess the progression of
myocardial infarction.
Ultrasound diagnosis has the potential to detect diastolic andsystolic dysfunction in the early stage of ischemic cascade.4,5)
Ultrasound-based measurements of myocardial strain andstrain rate (SR) have been developed to evaluate regional
myocardial function.6–11) The myocardial strain and SR,
obtained by removing the whole motion of the heart wall,
represent the change in the myocardial thickness. Previous
studies have indicated the possibility of identifying myocardialischemia12–14) or myocardial infarction15–17) using myocardial
strain and SR as well as the importance of the transmural
locality of the strain and SR measurements.18–20) The improvement of the locality of the strain and SR measurements
may help reveal contractions in the layered myocardium andclinical application for ischemic heart diseases.
Myocardial contractile response, caused by electrical excitation, has been studied to detect myocardial ischemia in its
early stages. It is well known that the conduction of electricalexcitation in the heart wall activates the myocardial contractile
response21) and causes complex dynamics. The propagation of
the myocardial contractile response has been conﬁrmed bymeasuring the myocardial velocity,22–25) displacement,26,27)
strain,28,29) and SR30) around the time phase representing theonset of the conduction of electrical excitation. It has beensuggested that myocardial ischemia causes an abnormal
propagation of the myocardial contractile response.23,28,29)
However, the propagation established by measuring thedisplacement or strain waveforms, obtained by integrating thevelocity or SR waveforms, might contain not only the
myocardial contractile response caused by electrical excitation but also other components because several natural
mechanical waves propagate in the heart wall during thisshort time phase.22,31,32) The changes caused by large natural
mechanical waves in the displacement or strain waveform
may be dominant than those caused by the minute myocardial
contractile response. Moreover, the myocardial velocity anddisplacement contain the whole motion of the heart wall;
however, the myocardial strain and SR do not contain them.
Thus, myocardial SRs in the heart wall can capture thepropagation of the myocardial contractile response in detail.
As the myocardial SRs are calculated using the velocities
obtained at multiple positions in the heart wall, local velocity
estimation is essential for the local measurement of SR. In
previous studies,7,30,33–35) the transmural SR distribution wasmeasured at different depths in the heart wall with hightemporal resolution using the phased-tracking method.36)
However, it has been difﬁcult for the conventional velocity
estimator36) to measure the minute changes in the spatially local
myocardial thickness because the estimated velocity is averaged
spatially by the cross-correlation function. We proposed themultifrequency phased-tracking method to improve the localityof the velocity estimation.37) Using the proposed local velocity
estimator,37) minute changes in the spatially local myocardial
thickness have been measured, which exhibit alternate layers ofcontraction and relaxation.38)
Two-dimensional distribution of myocardial SR, with highdensity beam scans, is required to obtain the propagation of theminute changes in the local myocardial thickness. The twodimensional SR distribution was measured to visualize thepropagation of the contraction and relaxation in the heartwall.30) In this study, low-density (sparse) beam scanning24,30)
was applied to locally measure the SR to realize a high-framerate measurement using a focused wave. Additionally, a
conventional velocity estimator with an averaging operation in
the depth direction was used. However, the low-density beamscans and the low-locality SR measurement challenged thedetailed measurement of the propagation of the minute change
in the local myocardial thickness in the lateral direction.
In the present study, we measured the two-dimensional
distribution of the myocardial SR with high-density beamscans, using the multifrequency phased-tracking method. The
propagation of the minute change in the spatially local
myocardial thickness was observed in the two-dimensional

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distribution of the myocardial SR, around the time phaserepresenting the onset of the conduction of electrical excitation, to reveal the mechanism of the effective contraction of
the heart. We discuss the measured propagation of the local
and minute contractile response in the SR distribution fromthe perspective of the physiological mechanism of the heart.
2. Methods
2.1. Ultrasonic measurement with high-density beamscans and high frame rate

Figure 1(a) shows the schematics of the low-density beamscans used in the previous study30) and high-density beamscans in the present study. To increase the density of theultrasound beam scans in the lateral direction compared withthat of the previous study,30) the spatial interval of theultrasound beams was set at 1.5°, wherein the density of
the ultrasound beam scans was more than three times higher
than that of the previous study (5.6°).
Measurement using a focused wave has a higher spatial
resolution than a plane wave or a diverging wave. Thus, theacquisition area of the radiofrequency (RF) signals waslimited to realize a dense measurement with a high frame
rate using a focused wave. The viewing angle of theacquisition area was reduced to 24°, compared with 45°
used in the previous study. In the measurements, the frame
rate, fFR , of the acquisition of the RF signals was set at503 Hz, which was 630 Hz in the previous study.30)

2.2. Measurement environment

In vivo measurements were applied to three healthy subjects
in their twenties using an ultrasound diagnostic apparatus.
The measurements were approved by the Ethics Committeeof Tohoku University. Additionally, all subjects agreed toparticipate in this study.
A focused wave was transmitted from a sector probe(UST-52105; Hitachi-Aloka-Medical Ltd., Tokyo, Japan)
connected to an ultrasound diagnostic apparatus (F75;
Hitachi-Aloka-Medical Ltd., Tokyo, Japan). The center
frequency of the transmitted wave was 3 MHz, and thesampling frequency fs was 20 MHz. Assuming that the speedof sound of the tissue, c0 , is 1540 m s−1, the spatial interval of
the sampling points in the ultrasound beam direction is0.038 mm. Electrocardiogram (ECG) and phonocardiogram(PCG) waveforms were acquired simultaneously in themeasurements. For each subject, the ECG waveform wasmeasured for lead II using the three-point lead method, and
the PCG waveform was measured using a microphone
attached to the subject’s chest.
Figures 1(b) and 1(c) show the schematic of the in vivo
measurement and the B-mode image of the cross-section in
the parasternal long-axis view, respectively. The acquisitionarea of the RF signals was limited to the interventricular
septum (IVS) to realize a high-frame-rate measurement. In
the parasternal long-axis view, the mitral valve (MV) wasused as a landmark such that the right-side boundary of the

(a)

(b)

(c)

(d)

Fig. 1. (Color online) (a) Schematics of low-density beam scans and high-density beam scans. (b) Schematic of in vivo measurement. (c) B-mode image ofthe cross-section in parasternal long-axis view. (d) Schematic of calculating strain rate (SR).

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acquisition area was set by the ultrasound beam locatedabove the MV, as shown in Fig. 1(c).
2.3. Local velocity estimation using multifrequency
phase differences37)
In the present study, the local velocity in the ultrasound beam
direction was estimated at multiple positions in the heart wallusing the multifrequency phased-tracking method.37) The
process of local velocity estimation, presented as follows,
was based on that described by referring to Ref. 37.
The RF signal of the ith ultrasound beam in the nth frame,si (t , n ), was cut out around the mth position using a Hanningwindow (±1.50 mm). The frequency spectrum Si, m ( f , n ) was
obtained by applying discrete Fourier transform (DFT) to thewindowed signal, si, m (t , n ). In the (n + 1)th frame, thefrequency spectrum, Si, m ( f , n + 1), was also obtained by
employing the same procedure. The cross-spectrum between
consecutive frames, Ci, m ( f , n ), was calculated as
Ci, m ( f , n) = Si*, m ( f , n) · Si, m ( f , n + 1) ,(1 )where * denotes the complex conjugate.
The phase gradient, ai, m (n ), of the cross-spectrum wasestimated by the least-square method using the amplitude of
the cross-spectrum, ∣ Ci, m ( f , n )∣, as a weighting function.
Assuming that the velocities in the window of the DFT arevd ,uniform between consecutive frames, the estimated velocity, 
between consecutive frames can be expressed using the estimated phase gradient, ai, m (n ), of the cross-spectrum as follows:vd (zi, m ; n) =c0 fFR· ai, m (n).
4p

the frequency-dependent attenuation and interference ofbackscattered waves can be suppressed.37) Thus, velocity
can be estimated locally without the spatial averaging
operation caused by the calculation of the cross-correlation
function.
2.4. Measurement of SR distribution in the heart wall
The myocardial SR distribution was calculated from thevelocities obtained at multiple positions in the heart wall. As
shown in Fig. 1(d), the SR on the mth position in the ith beam
was calculated as31,35,36)
SRi, m (n) =vd (zi, m +Dm ; n) - vd (zi, m -Dm ; n),∣ zi, m +Dm (n) - zi, m -Dm (n)∣(3 )where Dm is the interval of the sampling points used to
calculate the SR. In the present study, the initial interval∣ zi, m +Dm (0) - zi, m -Dm (0)∣ was set to 0.821 mm. The intervalin the nth frame, ∣ zi, m +Dm (n ) - zi, m -Dm (n )∣, was determinedby tracking the (m + Dm )th and (m - Dm )th positions,
respectively, by integrating the velocity waveform. The SRs
were obtained at several hundred positions in the depth
direction in each ultrasound beam, using which the twodimensional distribution of the SR was obtained.
In the parasternal long-axis view, it is assumed that theultrasound beam is perpendicular to the myocardial ﬁber
direction in each myocardial layer. As the myocardial
thickness increases (decreases) when the myocardium contracts (relaxes) in the ﬁber direction, the positive (negative)
SRs indicate myocardial contraction (relaxation).

(2 )3. Results

Here, zi, m is the depth of the mth position in the ith beam andc0 is the speed of sound of the living tissue.
As the phase gradient of the cross-spectrum is estimatedusing the multifrequency phase differences, the inﬂuence of

3.1. Two-dimensional distribution of myocardial SR
using local velocity estimator

Figure 2 shows the two-dimensional distribution of the
myocardial velocity and SR of the IVS at several time phases

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Fig. 2. (Color online) (a)–(d) Two-dimensional distributions of velocity of the ultrasound beam and (e)–(h) two-dimensional distributions of SR at several
time phases in a cardiac cycle. (i) Electrocardiogram (ECG) waveform. (j) Phonocardiogram (PCG) waveform. (k) M-mode image in the central beam.

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in a cardiac cycle. The blue and red colors in the velocity
distribution represent the velocity toward the left ventricular(LV) and right ventricular (RV), respectively. In the SR
distribution, the cold and warm colors represent the myocardial contraction and relaxation, respectively. At the time of
the ECG P-wave, the values of the SR in the IVS wereapproximately zero; i.e. the myocardia in the IVS did notcontract. However, at the time of the ECG R-wave, the SR
distribution shows alternate layers of contraction and relaxation, especially on the apical side. However, the velocity
distribution does not show the layers, as shown in Fig. 2(b).
In a previous study using the multifrequency phasedtracking method,38) the alternate layers of contraction andrelaxation were observed clearly in each ultrasound beam. In
the present study, similar alternate layers of contraction andrelaxation were conﬁrmed in each ultrasound beam.
Moreover, the alternate layers were measured as spatiallycontinuous in the longitudinal direction of LV, as shown in
Fig. 2(f), although the myocardial SRs were calculated
independently for each ultrasound beam. This continuity of
SR distribution in the longitudinal direction indicated that thealternate layers of contraction and relaxation reﬂect thephysiological mechanism of the heart.
Figure 3 shows the SR distribution at the time of the ECG
R-wave in three consecutive heartbeats for three subjects.
The alternate layers of contraction and relaxation, continuous
in the longitudinal direction, were observed for all thesubjects and their heartbeats.
3.2. Propagation of local and minute myocardial
contractile response
The two-dimensional distributions of SR were measured
around the time phase of the ECG R-wave. Figure 4 shows
the two-dimensional SR distributions every 2 ms for subject
A around the time phase of the ECG R-wave. At −14 msfrom the ECG R-wave, a rapid contraction (cold color) of the
myocardium was observed in several myocardial layers on
the apical side of the LV side of the IVS, as shown in
Fig. 4(a). Then, the rapid contraction propagated from theapical side to the basal side in the longitudinal direction until
the time of the ECG R-wave and the contractile region
gradually increased after the ECG R-wave. Although thesame SR pattern was not obtained even for three consecutive
heartbeats for the same subject, the propagation of the rapid
contraction from the apical side to the basal side followed thesame pattern.
Figures 5 and 6 show the two-dimensional distributions of
the myocardial SR around the time phase of the ECG R-wave
every 2 ms for subjects B and C, respectively. As shown in
Figs. 5 and 6, the rapid contraction on the LV side of the IVS
propagated from the apical side to the basal side for subjects
B and C, similar to that observed in subject A. Especially on
the LV side of the IVS, the propagation of the rapid
contraction in the longitudinal direction was conﬁrmed forall subjects.
4. Discussion
4.1. Usefulness of local and dense measurement of
two-dimensional distribution of myocardial SR

In a previous study that used the multifrequency phasedtracking method,38) the alternate layers of contraction andrelaxation were conﬁrmed in each ultrasound beam aroundthe time phase representing the onset of the conduction ofelectrical excitation. However, the relationship between thealternate layers and the physiological mechanism of the heart
were not discussed because of the low-density beam scans. In
the present study, high-density beam scanning enabled the
local and dense measurement of the two-dimensional distribution of alternate layers of contraction and relaxation andthe propagation of the rapid contraction in the longitudinal
direction of LV. These local and minute contractile responses
were captured by the local SR measurement but could not be
conﬁrmed by velocity measurement.
Similar SR patterns were measured in three consecutive
heartbeats for the same subject, although the patterns did notcompletely correspond. As the local SR reﬂects the minutechange in the local myocardial thickness, subtle changes in

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

Fig. 3. (Color online) Two-dimensional distributions of SR during the electrocardiogram (ECG) R-wave in three consecutive heartbeats with three subjects.

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(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

Fig. 4. (Color online) (a)–(l) Two-dimensional distributions of SR around time phase of electrocardiogram (ECG) R-wave every 2 ms for subject A. (m)ECG waveform. (n) Phonocardiogram (PCG) waveform.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

Fig. 5. (Color online) (a)–(l) Two-dimensional distributions of SR around time phase of electrocardiogram (ECG) R-wave every 2 ms for subject B. (m)ECG waveform. (n) Phonocardiogram (PCG) waveform.

the cross-section might affect the local SR measurement inconsecutive heartbeats. This effect of the subtle change in the
cross-section will be examined in a future study.
4.2. Relationship between alternate layers of contraction and relaxation and physiological mechanismof heart
Let us discuss the relationship between the alternate layers ofcontraction and relaxation in the two-dimensional distributions of the myocardial SR and the physiological mechanismof the heart. The conducting system in the heart, such as theHis-bundle, bundle branch, and Purkinje ﬁber, allows theelectrical excitation to be conducted fast. The myocardialﬁbers in the IVS are activated by the electrical excitationfrom the Purkinje ﬁbers connected to the bundle branch.
First, in the LV, the apical side of the IVS is activated by theleft bundle branch, which runs over the entire surface of the
IVS.21,39) Electrical excitation then occurs in the myocardium. The conduction speed of electrical excitation along the
myocardial ﬁber is 2–4 times faster than that across the
myocardial ﬁber.40) Thus, the conduction of the electrical

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(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

Fig. 6. (Color online) (a)–(l) Two-dimensional distributions of SR around time phase of electrocardiogram (ECG) R-wave every 2 ms for subject C. (m)ECG waveform. (n) Phonocardiogram (PCG) waveform.

excitation depends on the orientation of the myocardial
ﬁber.41,42) As the LV is constructed with a continuous
myocardial band that forms a complex spiral from the basalside to the apical side,43,44) the heart wall has a layered
structure of myocardial sheets in the transmural direction, andthe orientation of the myocardial ﬁber is different in thetransmural direction.18,45,46) Thus, electrical excitation conducts spirally in the LV along the myocardial ﬁbers in eachlayer.47)
In the present study, it was conﬁrmed that the contractile
response propagated in the longitudinal direction on the LVside of the IVS, which corresponds to the result in theprevious study on animal models that the endocardial
myocardium contracts earlier than the epicardial myocardium
around the time phase of the ECG R-wave.48) As the
direction of the myocardial ﬁber on the LV side of the IVS
is similar to the longitudinal direction,18,45,46) the propagationof the contractile response in the longitudinal direction
indicates that the electrical excitation was conducted along
the myocardial ﬁber direction. Considering the electricalexcitation conducts spirally in the LV along the myocardialﬁbers in each layer, the electrically activated time of the
myocardium may be different for each layer in the transmural
direction. Thus, the differences in the electrically activatedtime might have caused the alternate layers of contraction andrelaxation, as highlighted by the results of this study.
The mechanism of effective contraction in the layered
myocardium was clariﬁed by the alternate layers of contraction and relaxation observed in the local SR distribution.
These alternate layers of contraction and relaxation may
cause transmural shearing deformation at the boundary
between the layers, which occurs due to the layered structureof the myocardial sheets and helps thicken the heart wall
effectively.49,50) In the present study, the alternate layers ofcontraction and relaxation suggested transmural shearing

deformation, which realizes the rapid increase in the internalpressure of the LV in the transition period from diastole tosystole.
4.3. Transmitted wave condition for measurementwith high-density beam scans and high frame rate
The acquisition area of the RF signals was limited to the partof the IVS to realize the dense and local measurement in thelateral and beam directions with a high frame rate using a
focused wave. This measurement condition can be achieved
using existing commercial ultrasonic diagnostic apparatuses
and can thus be easily applied in clinical applications.
However, the acquisition area (24°) was not sufﬁcient toevaluate the entire LV region, as shown in Fig. 1(c)(approximately 90°). Although the propagation of the local
and minute contractile response could be measured in thelimited acquisition area in the present study, the measurement
condition in the present study may not always be optimal.
Alternatively, the parallel beamforming method using aplane wave or a diverging wave may be useful for measuring
a larger area densely in the lateral direction.51–53) Thesetransmitted wave conditions allow us to expand the measurement region with a higher frame rate than that with a focusedwave used in the present study. The local SR measurement
can also be applied to measurements using a plane wave or
diverging wave. However, measurements using a plane wave
or diverging wave have a lower spatial resolution and signalto-noise ratio than those using a focused wave,54) and theparallel beamforming method requires sufﬁcient computational capacity. Thus, there is a trade-off relationship related
to the transmitted wave conditions. Therefore, a suitabletransmitted wave condition must be determined by considering the measurement region, spatial and temporal resolution, and feasibility of clinical application in future studies. It
is also necessary to clarify the physiological mechanism of
the heart to determine a suitable transmitted wave condition.

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4.4. Clinical application for evaluating transmuralityof myocardial ischemia

Alternate layers of contraction and relaxation were observedin the local SR distribution in healthy subjects. This may
have been caused by the conduction of electrical excitation
along the myocardial ﬁber direction. Abnormal conduction ofelectrical excitation in myocardial ischemia causes a delay inthe contractile response,23,28,29) and the local SR pattern may
change owing to the delay of the contractile response. Thus,
local SR distribution can visualize the transmurality of
myocardial ischemia. The differences in the local SR pattern
between healthy subjects and patients will be examined in a
future study.
There is a limitation in local SR measurements. As themultifrequency phased-tracking method improves the localityof the SR measurement in the ultrasound beam direction,37)
the ultrasound beam direction corresponds to the transmural
direction of the heart wall to realize the local measurement in
the transmural direction. Thus, the measurement view islimited, depending on the evaluation. To evaluate thetransmurality of myocardial ischemia locally, basal-septal,
basal-lateral, mid-septal, and mid-lateral walls can be measured in the parasternal long-axis or short-axis view, apicalseptal and lateral walls can be measured in the parasternal
short-axis view, and the apex can be measured in the apicalview. However, the local SR measurement of the anterior andinferior walls may be difﬁcult because the ultrasound beam
direction does not correspond to the transmural direction inthese measurements. The 17-segment model of the LV isgenerally used for the assessment of wall motion.55) It isdifﬁcult to evaluate the transmurality of myocardial ischemia
using the local SR measurement in the anterior segments(1, 7, and 13) and the inferior segments (4, 10, and 15) in the
17-segment model.
5. Conclusions

The two-dimensional distributions of the myocardial SR,
measured with high-density beam scans using our proposed
local velocity estimator, exhibited alternate layers of contraction and relaxation around the time phase, representing theonset of the conduction of electrical excitation. The propagation of the local and minute contractile response along the
myocardial ﬁber on the LV side of the IVS was captured forthree healthy subjects. The results indicated the effective
mechanism of the transition process from diastole to systole,
where transmural shearing deformation occurs between thealternate layers of contraction and relaxation. The evaluationof the myocardial SR needs to consider the inﬂuence ofalternate layers of contraction and relaxation to detect
myocardial ischemia in its very early stages by measuring
the contractile response caused by electrical excitation. The
measurement of myocardial SR, with high-density beamscans, using the multifrequency phased-tracking method,
can reveal the effective contraction with transmural shearing
deformation and determine the appropriate evaluation index
of the contractile function in the layered myocardium.
Acknowledgments

This work was supported in part by JSPS KAKENHI
19K22943.

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