Ultrasound in Med. & Biol., Vol. 47, No. 9, pp. 27682773, 2021
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https://doi.org/10.1016/j.ultrasmedbio.2021.05.021

 Technical Note
STRAIN RATE DISTRIBUTION IN LAYERED MYOCARDIUM MEASURED USINGLOCAL VELOCITY ESTIMATOR WITH MULTIFREQUENCY PHASE DIFFERENCES
AGEDPYT U OBARA,* SHOHEI MORI,y

MOTOTAKA ARAKAWA,*,y and HIROSHI KANAI*,yTAGEDEN* Graduate School of Biomedical Engineering, Tohoku University, Sendai, Japan; and y Graduate School of Engineering, Tohoku
University, Sendai, Japan(Received 11 November 2020; revised 5 May 2021; in final form 25 May 2021)

Abstract—Measurement of the myocardial strain rate (SR), with high spatial resolution, is useful in evaluation of
the transmurality of myocardial infarction. As the SR distribution is calculated using velocities observed at multiple positions in the heart wall, it is necessary to estimate the local velocity to measure SR distribution. In the present study, our previously proposed local velocity estimator, with multifrequency phase differences, was used tomeasure SR distribution in the heart wall. The SR distribution measured with the proposed local velocity estimator revealed alternate layers of contraction and relaxation, which were not measured with the conventional velocity estimator with spatial averaging. The reproducibility of the SR distributions was confirmed in threeconsecutive heartbeats with three subjects. High-spatial-resolution SR measurement with the proposed local
velocity estimator will allow myocardial layer-specific analysis in the transmural direction. (E-mail: mori@ecei.
tohoku.ac.jp) © 2021 World Federation for Ultrasound in Medicine & Biology. All rights reserved.
Key Words: Ultrasound, Heart wall, Strain rate, Layered myocardium, Phase difference.

In a previous study, we proposed a velocity estimator, with multifrequency phase differences, to estimate
the local velocity without spatial averaging(Obara et al. 2021). As this velocity estimator could alleviate the negative effects of the attenuation in propagation in the living tissue and the interference caused by
the superposition of backscattered waves from multiple
myocardial fibers, the local velocity in the heart wall
was measured without a window for averaging (Obaraet al. 2021). The precision of the local velocity estimation was confirmed, and the usefulness for measuring the
myocardial SR distribution was discussed in that study.
However, this velocity estimator has not yet been
applied to the measurements of SR distribution.
In the present study, the myocardial SR distribution
in the transmural direction for healthy subjects was measured using the conventional velocity estimator, with asingle-frequency phase difference, and the proposed
velocity estimator, with multifrequency phase differences. To discuss the relationship between the locality ofthe velocity estimation and the SR distribution in thetransmural direction, we compared the spatial distributions of SR measured using a velocity estimator without
spatial averaging and those with spatial averaging.

INTRODUCTION
Ultrasound-based measurements of myocardial strain
rate (SR) have been studied to evaluate regional myocardial function. The regional SR is useful for defining thetransmurality of myocardial infarction (Weidemannet al. 2003). Myocardial layer-specific analysis has been
conducted to detect myocardial infarction in very earlystages (Norum et al., 2015; Rimbaş et al. 2020). Therefore, high-spatial-resolution SR measurement has thepotential to detect local abnormalities in the transmural
direction.
In previous studies, myocardial SR distributions
were measured using ultrasound (Sutherland et al. 2004;
Tanaka et al. 2014). As the SR distribution is calculatedusing the velocities at multiple positions in the heartwall, it is important to estimate local velocities for SR
measurement with high spatial resolution. However,ultrasound-based velocity estimators typically require
spatial and/or temporal windows for averaging(Kanai et al. 1997).

Address correspondence to: Shohei Mori, Graduate School ofEngineering, Tohoku University, Sendai 980-8579, Japan. E-mail:mori@ecei.tohoku.ac.jp

2768Proposed velocity estimator for strain rate distribution  Y. OBARA et al.

METHODS
Subjects
Three healthy subjects aged between 20 and 29
agreed to participate in this study. The human study protocol was approved by the ethics committee of Tohoku
University, and the individuals agreed to participate inthis study.

Ultrasound data acquisition
In vivo measurements were applied to the interventricular septum (IVS) in the parasternal long-axis view(Fig. 1a) using an ultrasound diagnostic apparatus.
Focused waves with a center frequency, fc , of 3.75 MHz
were transmitted from a sector probe (UST-160 52101;
Hitachi-Aloka-Medical Ltd., Tokyo, Japan) connected toan ultrasonic diagnostic apparatus (SSD 6500; HitachiAloka-Medical Ltd.). The sampling frequency, fs , was
20 MHz. The interval between the sample points was
0.038 mm, assuming that the sound velocity in living tissue is 1540 m/s.
A previous study measuring the myocardial SR distribution focused on the propagation of contraction
caused by the conduction of electrical excitation(Yoshiara et al. 2007). Considering that the conduction
speed of electrical excitation in the vertical direction of
the myocardial fiber, that is, the transmural direction of
the heart wall, is 80200 mm/s (Sano et al. 1959), theframe rates, fFR , were set at 630 Hz for subjects A and B
and 425 Hz for subject C by reducing the number ofultrasound beams in acquiring the ultrasound data.

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Physiological data acquisition
For each subject, the electrocardiogram (ECG)
waveform was measured for lead II using the three-point
lead method. The phonocardiogram (PCG) waveform
was measured simultaneously using a small microphone
attached to the subject’s chest.
Measurement of myocardial SR distribution
In the present study, the measurement of the myocardial SR distribution was applied to the time phasearound the R-wave in the ECG, which is associated withthe onset of the myocardial contraction. The region of
the IVS was manually segmented, and the radiofrequency data on the beam that was parallel to the transmural direction of the IVS were analyzed (Fig. 1a). The
analysis was processed offline using our own developed
software on a Linux system.
The conventional velocity estimator, with a singlefrequency phase difference (Kanai et al. 1997), and ourpreviously proposed velocity estimator, with multifrequency phase differences (Obara et al. 2021), wereapplied to radiofrequency data to estimate the velocities
at multiple positions on the heart wall. In the conventional velocity estimator, the spatial averaging by thecross-correlation function was needed to alleviate thenegative effects of the attenuation in propagation in theliving tissue and the interference caused by the superposition of backscattered waves from multiple myocardial
fibers. Our previously proposed velocity estimator does
not require the spatial averaging operation because thisestimator can alleviate these negative effects using multifrequency phase differences weighted by the amplitudeFig. 1. (a) B-mode image of the cross-section where the ultrasound data were acquired in the parasternal long-axis view.
(b) Schematic of the measurement of myocardial strain rate (SR) distribution. DFT = discrete Fourier transform;
IVS = interventricular septum; LV = left ventricle; RV = right ventricle.

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Ultrasound in Medicine & Biologyof the cross-spectrum between two consecutive frames.
The local velocity estimation without spatial averaging
is useful to measure the heart wall dynamics where thechange in thickness occurs.
In both velocity estimators, the velocities were estimated under two different conditions, as illustrated in
Figure 1b. Condition (i) was without spatial averaging
by the cross-correlation function. Thus, its window
length corresponded to the Hanning window for the discrete Fourier transform (DFT) in the velocity estimation(2.5 mm). Condition (ii) was with spatial averaging by
the cross-correlation function (Kanai et al. 1997). The
total window length in condition (ii) was 5.0 mm.
The SR distribution was obtained by calculating the
SR using the velocities at two positions. The SR at themth position at time t was calculated as(Tanaka et al. 2014)
SRm ðtÞ ¼

vd ðzmþ1 ; tÞ  vd ðzm ; tÞ:jzmþ1 ðtÞ  zm ðtÞjð1ÞHere, zm ðtÞ is the depth of the mth position, and vd ðz; tÞ isthe velocity in the beam direction at depth z. The initialinterval jzmþ1 ð0Þ  zm ð0Þj for calculating the SR was
0.82 mm used in a previous study (Tanaka et al. 2014).
Evaluation for reproducibility of SR distribution inlayered myocardium
The reproducibility of SR distribution was evaluated around the time of the R-wave in the ECG in three

Volume 47, Number 9, 2021

consecutive heartbeats. We calculated the standard deviation (SD) among three consecutive heartbeats in the SR
distributions to compare quantitatively the reproducibility in the conventional method with that in the proposed
method. The region of interest (ROI) for calculating the
SD was set at a region of 40 ms  5 mm on the mid-IVS
on the M-mode image. The SDs among three consecutive heartbeats were calculated for every depth and time(frame) in the ROI, and SDs in the ROI were averaged.
RESULTS
Figure 2a illustrates the M-mode image of the IVS
during the time phase around the R-wave in the ECG,
where the yellow lines represent the tracking points on
the right ventricular and left ventricular sides of the IVS.
Figure 2be illustrates the SR distribution in the
IVS measured using the conventional (single-frequency)
and proposed (multifrequency) velocity estimators. The
positive and negative SRs measured in the parasternal
long-axis view indicated the increase and decrease in the
thickness of the cross-fiber direction, respectively. Considering the volume conservation law, the increase(decrease) in the thickness indicated the contraction(relaxation) of the myocardial fiber. In Figure 2be, thecold (warm) color represents the increase (decrease) in
the thickness, indicating contraction (relaxation).
The SR distributions, measured using the velocity
estimators without spatial averaging, reveal alternate
layers of contraction and relaxation, as shown in

Fig. 2. (a) M-mode image of the interventricular septum (IVS). (b) Strain rate (SR) distribution measured with the conventional velocity estimator, using a single-frequency phase difference, without spatial averaging. (c) SR distribution
measured using the conventional velocity estimator with spatial averaging. (d) SR distribution measured with the proposed velocity estimator, using multifrequency phase differences, without spatial averaging. (e) SR distribution measured with the proposed velocity estimator with spatial averaging. (f) Electrocardiogram (ECG) waveform. (g)Phonocardiogram (PCG) waveform. LV = left ventricle; RV = right ventricle.

Proposed velocity estimator for strain rate distribution  Y. OBARA et al.

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Fig. 3. (a) M-mode image of the interventricular septum (IVS) in heartbeat 1. (bd) Strain rate (SR) distributions measured using the proposed velocity estimator without spatial averaging for (b) heartbeat 1, (c) heartbeat 2, and (d) heartbeat 3, respectively. (e) Electrocardiogram (ECG) waveform. (f) Phonocardiogram (PCG) waveform. LV = left
ventricle; ROI = region of interest for calculating the averaged standard deviation in the SR distributions; RV = rightventricle.

Figure 2b, 2d. Although no temporal window was used
for averaging, this multilayered pattern of the SR distribution measured by the proposed local velocity estimator
was continuous between the rising time of the R-wave in
the ECG and the rising time of the first heart sound in
the PCG, which represented the start of the ejection
phase (Fig. 2d). In the velocity estimators with spatial
averaging, this multilayered pattern did not appear, as
shown in Figure 2c, 2e, similarly to the previous study

using the conventional velocity estimator with spatial
averaging (Tanaka et al. 2014).
The reproducibility of the SR distribution measured
using the conventional and proposed velocity estimators
without spatial averaging was evaluated in three consecutive heartbeats for three healthy subjects. Figure 3
illustrates the SR distributions measured by the proposed
local velocity estimator for subject A for three consecutive heartbeats. The values of averaged SDs among threeFig. 4. (a) Strain rate (SR) distribution measured using the proposed velocity estimator without spatial averaging for
subject B. (b) Electrocardiogram (ECG) waveform for subject B. (c) Phonocardiogram (PCG) waveform for subject B.
(d) SR distribution measured using the proposed velocity estimator without spatial averaging for subject C. (e) ECG
waveform for subject C. (f) PCG waveform for subject C.

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Ultrasound in Medicine & Biology

consecutive heartbeats in the SR distributions were 8.4(conventional method) and 1.9 (proposed method) insubject A. Figure 4 illustrates the SR distributions for
subjects B and C. The values of the averaged SDs were
5.8 (conventional method) and 1.2 (proposed method) insubject B and 9.2 (conventional method) and 3.7 (proposed method) in subject C. In three subjects, the valuesof the averaged SD in the proposed method were smaller
than those in the conventional method. Therefore, theproposed method was more reproducible than the conventional method.
DISCUSSION
We discussed the relationship between the localityof the velocity estimation and the multilayered pattern of
the SR distribution. As shown in Figure 2, the multilayered pattern of SR distribution was measured using avelocity estimator without spatial averaging and was notmeasured using that with spatial averaging. The velocities in the heart wall contain the large velocity caused by
the whole motion of the heart wall and the minute velocity caused by the change in the local myocardial layer
thickness. In averaging the velocities spatially, the local
and minute changes in thickness may be suppressed as
the variance of velocities in the window of the velocity
estimation, and the velocity caused by the whole motionof the heart wall is estimated. Thus, the layered pattern,
as well as the number and thickness of layers in the SR
distribution, might depend on the locality of the velocity
estimation. As the calculation of the cross-correlation
function causes the spatial averaging operation weighted
by the amplitude of the analyzed signal, it is not suitable
for the layer-specific analysis in the transmural directionof the heart wall. In previous studies such as the Mmode tissue Doppler imaging technique or the conventional velocity estimator, a single-frequency phase difference was used and more homogeneous SR
distributions in the transmural direction were measured(Derumeaux et al. 2000; Tanaka et al. 2008). As thesevelocity estimators typically require spatial averaging,
the homogeneous SR distributions have resulted fromthe effects caused by the spatial averaging.
As discussed in a previous study, the conventional
velocity estimator is affected by the negative effects of
the attenuation in propagation in the living tissue and theinterference caused by the superposition of backscattered
waves
from
multiplemyocardial
fibers(Obara et al. 2021). Thus, the averaged SD in the local
SR distribution measured using the conventional velocity estimator was large compared with that using the proposed velocity estimator which can alleviate thenegative effects. Thus, the proposed velocity estimatorwith multifrequency phase differences is needed forVolume 47, Number 9, 2021

estimating precisely the local velocity without the crosscorrelation function (Obara et al. 2021).
However, it could not be validated whether the
reproducibility evaluated by the SD of the SR distribution measured using the proposed method is sufficient or
not for in vivo measurement, and this is our future work.
Moreover, the accuracy of the proposed method has notbeen evaluated by comparing it with the “true” velocity
or SR. The accuracy evaluation allows the discussions
about the limitation of locality and the suitable window
length for measuring the SR distribution. These concerns
will be validated and discussed in our future studies.
High-spatial-resolution SR measurement in thetransmural direction using the proposed local velocity
estimator applies to the region where the ultrasoundbeam corresponds to the transmural direction of the heartwall. Thus, the measurement view is limited dependingon the region of the heart to set the ultrasound beam
direction along the transmural direction.
In the present study, high-spatial-resolution SR
measurement in the transmural direction was used inhealthy subjects. The SR distribution measurement for
an abnormal subject and the comparison of the resultwith that in the healthy subject may allow discussion of
the relationship between the alternate layers of contraction and relaxation with the electromechanical and physiological mechanism of the heart. Elucidation of thephysiological role of the alternate layers is important todetermine whether these layers are related to the actual
contractile response of the layered myocardium or not. It
is our future work to measure the SR distribution of anabnormal subject.
CONCLUSIONSTo measure the myocardial SR distribution withhigh spatial resolution in the transmural direction, theproposed local velocity estimator was applied to themeasurements of SR distribution. The local measurement using the proposed velocity estimator with multifrequency phase differences was more reproducible thanthat using the conventional velocity estimator with a single-frequency phase difference. The SR distribution
revealing alternate layers of contraction and relaxation
was observed in the proposed method by improving the
locality of the velocity estimation. High-spatial-resolution SR measurement using the proposed local velocity
estimator will allow myocardial layer-specific analysis
in the transmural direction.
Acknowledgments—This work was supported in part by Japan Society
for the Promotion of Science KAKENHI Grants 19K22943 and
19KK0100.
Conflict of interest disclosure—The authors declare that they have nocompeting interests.

Proposed velocity estimator for strain rate distribution  Y. OBARA et al.

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