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Japanese Journal of Applied Physics 56, 07JF09 (2017)https://doi.org/10.7567/JJAP.56.07JF09

Identiﬁcation of the heart wall and chamber based on temporal changeof ultrasonic scatterer distribution
Kohei Takahashi1, Hirofumi Taki1,2, 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: kanai@ecei.tohoku.ac.jp
Received November 24, 2016; accepted March 6, 2017; published online June 12, 2017
In most current methods for evaluating the cardiac function by ultrasound, the heart wall area is identiﬁed manually by an examiner. To eliminate
examiner dependence and to improve usability, an automatic heart wall identiﬁcation method is desirable. Identiﬁcation based on only echogenicity
often fails because of low echogenicity of some areas of the heart wall. In the present study, to determine more essential features, we focused on
the relative temporal change of ultrasonic scatterer distribution and proposed three features for identiﬁcation of the heart wall and the chamber:cross-correlation of RF signals, that of envelopes, and spatial dispersion of movement vectors in small regions. In an in vivo experiment, using
echogenicity and the three features, we identiﬁed the heart wall and the chamber in the left ventricular long-axis view, resulting in criteria ofseparability J of 1.69, 1.40, and 3.02 using these features compared with the result of 0.979 using echogenicity.
© 2017 The Japan Society of Applied Physics

1.

Introduction

Echocardiography is useful for the screening of diseases
because of its noninvasiveness, low cost, and repeatedapplicability.1–3) In addition, quantitative evaluation of
myocardial function by ultrasound has been developed forthe early detection of cardiac diseases. For example, ultrasound Doppler measurements with high temporal resolution
have been developed to evaluate intracardiac blood ﬂow4)
and cardiac wall motion.5) Methods of evaluating twodimensional cardiac wall motion and strain rate by theultrasound speckle tracking method have also been reported.6–12) Ultrasound measurement with high temporal
resolution also enables imaging of the vibration propagation
caused by closure of the heart valve and contractile responseby electrical excitation.12–15)
In most of these methods, the heart wall area, which is theobject to be analyzed, is manually identiﬁed in a crosssectional image of the heart. Alternatively, to eliminate
examiner-dependence and to improve usability, an automaticheart wall identiﬁcation method is strongly desired. Several
researchers have proposed automatic or semi-automatic
identiﬁcation methods using echogenicity to distinguishregions of the heart wall from the chamber.16–18) However,
the echogenicity of the heart wall changes owing to temporalvariation of the direction of the myocardial ﬁber19) and themismatch of acoustic impedance,20) sometimes resulting in
the appearance of hypogenic areas in the heart wall during a
cardiac cycle. Therefore, high-accuracy identiﬁcation of theheart wall based on only echogenicity is diﬃcult.
As a solution to this problem, some identiﬁcation methods
using features other than echogenicity have been developed.
These methods use not only the information in each frame
but also the information of consecutive frames. Dydenko
et al. proposed a boundary detection method utilizing thediﬀerence of velocity between that in the heart wall and thatin the chamber.21) Other researchers have proposed identiﬁcation methods utilizing the diﬀerences of cross-correlationof the received signals between frames, resulting in improvement of the identiﬁcation of the heart wall in ejection andﬁlling phases.22,23) For identiﬁcation of the heart wall and thechamber, Kinugawa et al. proposed using the magnitudesquared coherence (MSC) function, which evaluates thevariance of the phase shift of the radio frequency (RF) signals
between consecutive frames.24) Takahashi and Nakahara
et al. proposed a method utilizing echogenicity and MSC,
which improved results of identiﬁcation in the slow ﬁllingphase.25–27) These methods showed the eﬀectiveness offeatures other than echogenicity for identiﬁcation. Achievement of high-accuracy identiﬁcation, however, has been
restricted to the cardiac phase: the transition period from therapid ﬁlling phase to the slow ﬁlling phase, which isrelatively easy to identify. Herein, more essential features fordiﬀerentiation of the heart wall from the chamber during a
cardiac cycle are proposed.
2.

Principle

A method to identify the heart wall and the chamber which
focuses on the temporal change of scatterer spatial distribution is herein proposed as follows.
2.1 Temporal change of scatterer spatial distribution
In the heart wall, major scatterers are intercellular substancesconsisting of collagen ﬁbers. These scatterers exist between
myocardial bundles, and the solid structure of these bundles
maintains the scatterer spatial distribution. In the chamber,on the other hand, major scatterers are red blood cells.
Figure 1 shows a schema of temporal change of scatterer
spatial distribution in the heart wall and the chamber. The
heart wall has translational motion28,29) corresponding tocontraction and relaxation and motion which is caused by
the change in thickness.7–11) Translational motion shifts RF
signals to the direction of the motion, and thickness change
causes temporal changes of the RF signal waveforms
because scatterer spatial distribution change. The shift ofRF signals, caused by translational motion can be canceledby the tracking method described below, and it can beassumed that the change in thickness during a short time
period is minute. In addition, in the left ventricular long-axis
view, scatterers in the heart wall mainly move in the axial
direction not in the lateral and elevational directions. The
axial direction can be followed by tracking the heart wall
because the tracking method employed in the present study

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Fig. 1. (Color online) Illustration of temporal change of scatterer distribution and RF signals.

Fig. 2. (Color online) Illustration of tracking method.

is highly accurate in estimating axial movement of the heartwall.
In the chamber, on the other hand, blood ﬂow with cardiac
motion causes large temporal changes in the RF signal
waveforms because the scatterer spatial distribution changes.
The blood ﬂow causes red blood cell scatterers in thechamber to move in lateral, axial, and elevational directions.30) Thus, the relative temporal change of scatterer spatial
distribution in the chamber should be suﬃciently larger thanthat in the heart wall when tracking is applied to the heartwall. Therefore, temporal change of RF signal waveforms in
the consecutive frames is suitable for diﬀerentiating the heart
wall from the chamber.
2.2 Tracking method
Figure 2 shows the tracking method employed in the present
study. As shown in the ﬁgure, Pði; j; nÞ denotes themeasurement point at lateral position i and axial position jin the n-th frame. The movement of each point Pði; j; nÞ isestimated from the cross-correlation between RF signals ofconsecutive frames in the search area, which is set withina circle centered on Pði; j; nÞ to be tracked. Moreover,k; a^ ki;j;n ; n þ kÞ denotes the estimated point of Pði; j; nÞ inPðl^i;j;nkthe (n + k)-th frame by the tracking method, where l^i;j;nandka^ i;j;n respectively show the estimated lateral and axial
positions at k frames after the point Pði; j; nÞ set at n-thframe. The displacement of the measurement point Pði; j; nÞfrom the n-th frame to the (n + 1)-th frame is described as
movement vector !xði; j; nÞ, which is deﬁned as follows:10!xði; j; nÞ ¼ Pðl^i;j;n; a^ 1i;j;n ; n þ 1Þ % Pðl^i;j;n; a^ 0i;j;n ; nÞ;ð1Þ

0
where Pðl^i;j;n; a^ 0i;j;n ; nÞ is equivalent to Pði; j; nÞ.
The tracking method calculates two-dimensional crosscorrelation in a cross-sectional image with lateral and axial
directions and is able to cancel the translational motions bothin the axial and lateral directions. Moreover, the translationalmotion in elevational direction can be neglected in the

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Fig. 3. (Color online) Illustration of envelopes in a small circular region.

present study, as described below. An acquired crosssectional image has a thickness in the elevational directionthat is equivalent to the beam width in the direction of thesector probe to be used. By increasing the frame rate so thatthe maximum displacement of the heart wall between
consecutive frames is suﬃciently smaller than the beamwidth in elevational direction, the same regions of the heart
wall are included in cross-sectional images of consecutive
frames. Therefore, the translational motion in the elevational
direction is neglected, and the motions both in axial andlateral directions can be cancelled by the tracking method.
2.3 Features for identiﬁcation
In the present study, for identiﬁcation of the heart wall andthe chamber, the following three features were introduced, allof which reﬂect the diﬀerences between the heart wall and thechamber in the small circular region between consecutive
frames.
2.3.1 Cross-correlations of RF signals and envelopes between consecutive frames. As illustrated inFig. 1, the temporal change of RF signal waveforms in thechamber is suﬃciently larger than that in the heart wall. To
detect the temporal change of RF signals, a cross-correlation
technique was applied to the RF signal and those envelopes
after the tracking process. The RF signals can evaluate thechange of waveforms more accurately by phase information
when tissue deformation is suﬃciently small. On the other
hand, the envelopes of the RF signals have the advantage ofbeing robust against the change of the RF waveforms whentissue deformation is large. According to the cross-correlation
error regarding the RF signals and those envelopes withtissue deformation, RF signals have fewer errors thanenvelopes when tissue deformation is under 0.1%, andenvelopes have fewer errors than RF signals when tissue
deformation is over 2%.31) Therefore, in the present study,
both cross-correlations are employed as follows.
A set of the envelope signals within a small circular regionkcentered on the point Pðl^i;j;n; a^ ki;j;n ; n þ kÞ is deﬁned askk^^envðl; a; Pðli;j;n ; ai;j;n ; n þ kÞÞ, as shown Fig. 3. Let us deﬁnekthe two-dimensional cross-correlation value Cenv ðl^i;j;n; a^ ki;j;n ;n þ kÞ with zero lag of the set of envelope signals withina small circular region centered on the tracked pointkPðl^i;j;n; a^ ki;j;n ; n þ kÞ between two consecutive frames fromthe (n + k)-th frame byk; a^ ki;j;n ; n þ kÞ
Cenv ðl^i;j;nk¼ corrfenvðl; a; Pðl^i;j;n; a^ ki;j;n ; n þ kÞÞ;envðl; a; Pðl^kþ1 ; a^ kþ1 ; n þ k þ 1ÞÞg;
i;j;n

i;j;n

ð2Þ

where corr{⋯} is the two-dimensional cross-correlation
function with zero lag. Moreover, the temporal averagek; a^ ki;j;n ; n þ kÞ among consecutive
Cenv,ave ði; j; nÞ of Cenv ðl^i;j;n2N frames is applied as follows:
N%1
X

Cenv,ave ði; j; nÞ ¼ k¼%N

k
½Cenv ðl^i;j;n; a^ ki;j;n ; n þ kÞ ' wðkÞ(
N%1
X

wðkÞ

; ð3Þ

k¼%N

where w(k) is a Hanning window function with a length of
2N. The averaged cross-correlation CRF,ave ði; j; nÞ of the RF
signals between consecutive frames is calculated in the same
way as the calculation of Cenv,ave ði; j; nÞ.
2.3.2 Dispersion of movement vectors. By applying
the tracking method, displacement between consecutive
frames is estimated as movement vector !xði; j; nÞ for every
discrete point Pði; j; nÞ. As illustrated in Fig. 4(a), themovement vector !xði; j; nÞ at each point in a small circularregion around Pði; j; nÞ in the heart wall can be assumed
to have similar components. In the chamber, however, themovement vector at each point in a small circular region
around Pði; j; nÞ has incoherent components because thesame regions cannot be tracked due to the change in the
scatterer spatial distribution. These phenomena are also valid
in one-dimensional space in the axial direction, as shownin Fig. 4(b).
Let us deﬁne the movement vectors in the axial direction
within a small circular region centered on the point Pði; j; nÞas vecðl; a; Pði; j; nÞÞ. To detect dispersion of the movement
vectors vecðl; a; Pði; j; nÞÞ in the axial direction, let us
calculate their standard deviations within a small circularkregion. The spatial standard deviation SDðl^i;j;n; a^ ki;j;n ; n þ kÞkk^^of vecðl; a; Pðli;j;n ; ai;j;n ; n þ kÞÞ in the (n + k)-th frame isdeﬁned as follows:kkSDðl^i;j;n; a^ ki;j;n ; n þ kÞ ¼ SDfvecðl; a; Pðl^i;j;n; a^ ki;j;n ; n þ kÞÞg;ð4Þ

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(a)

(b)

Fig. 4. (Color online) Illustration of movement vectors in a small circular region: (a) Lateral and axial directions. (b) Axial direction.

where SD{⋯} is the function calculating the standard
deviation. The temporal average SDave ði; j; nÞ ofkfSDðl^i;j;n; a^ ki;j;n ; n þ kÞg among consecutive 2N frames isdeﬁned as follows:

SDave ði; j; nÞ ¼

N%1
X

k¼%N

k
½SDðl^i;j;n; a^ ki;j;n ; n þ kÞ ' wðkÞ(
N%1
X

wðkÞ

:

ð5Þ

k¼%N

These features of Cenv,ave ði; j; nÞ, Cenv,ave ði; j; nÞ, andSDave ði; j; nÞ were employed to identify the heart wall andthe chamber as described in the next section.
2.4 Automatic identiﬁcation of heart wall andchamberIn the present study, the automatic method for identiﬁcationof the heart wall and the chamber was employed.27) At the
beginning, in order to reduce the clutter component from thesurrounding tissue, a moving target indicator (MTI) ﬁlter for
RF signals was applied as a high-path ﬁlter, its cut-oﬀ
frequency being 10 Hz.26,32) After MTI ﬁltering, the featuresdescribed above were calculated at all discrete points in all
frames and were spatially smoothed by adaptive mean (AM)ﬁltering.33,34) By the expectation-maximization (EM) algorithm,35) we classiﬁed the heart wall and chamber automatically and identiﬁed the areas of all frames in a cardiac cycle.
Using the EM algorithm, a mixture of two Gaussian distributions, which correspond to the heart wall and the chamber,
was ﬁtted to the features of all discrete points in a frame.
The threshold for the classiﬁcation of each data point wasdetermined where the two probabilities of the determined
Gaussian distributions had the same value.
In order to compare the classiﬁcation accuracy of the
proposed method with that of the conventional method using
echogenicity, criterion J of separability was introduced as afunction to evaluate classiﬁcation accuracy.36) By identifying
the interventricular septum (IVS) and the left ventricle (LV)manually, classiﬁcation accuracy between the two areas wasevaluated. Using the feature at each measurement point in

the IVS and the LV, the interclass covariance SB, whichcorresponds to the distance between means of classes wascalculated, as was intraclass covariance SW, which corresponds to the mean variance of features within classes.
Separability of the feature increased in proportion to the
distance between means of classes, whereas it decreased inproportion to the variances of features within classes.
Therefore, criterion J of separability was deﬁned by normalizing the interclass covariance SB by the intraclass covariance
SW as follows:
J¼

SB
:
SW

ð6Þ

2.5

In vivo measurement
In the present study, the heart of a healthy human subject
was measured in the left ventricular long-axis view during a
cardiac cycle (center frequency: 3.5 MHz; frame rate:
168 Hz; sampling frequency: 20 MHz). The measurement
intervals in the axial and time directions were 38.5 µm and5.95 ms, respectively, and the measurement interval in thelateral direction was 3.99 mm at the center position of theregion of interest (ROI). The −12 dB width of the ultrasonicbeam pulse was 0.50 mm, and that of the ultrasonic beam
was 9.0 mm, 12 mm in lateral and elevational directions,
respectively. Since the maximum velocity of the heart wallis less than 0.1 m=s,37) the maximum displacement of theheart wall between consecutive frames by translationalmotion is approximately 595 µm when the frame rate is
168 Hz. Therefore, the radius of the search area for the
tracking method was set at 595 µm. The translationalmotion in elevational direction of the heart wall could be
neglected because the maximum displacement of the heart
wall between consecutive frames was suﬃciently smaller
than the width of ultrasonic beam in the elevational
direction. For calculating the average cross-correlation ofenvelopes of Eq. (3) and average dispersion of movement
vectors of Eq. (5), the radius of the small region and thenumber of frames 2N were set at 1.8 mm and 18 frames,
respectively.

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(a)

(b)

(c)

(d)

(a)

(b)

(c)

(d)

Fig. 5. (Color online) Two images of left ventricular long-axis view: (a) B-mode image. (b) Average cross-correlation of RF signals. (c) Average crosscorrelation of envelopes. (d) Average spatial standard deviation of movement vectors. Periods A, B, C, D, E, and F denote the isovolumetric contraction phase,the ejection phase, the isovolumetric relaxation phase, the rapid ﬁlling phase, the slow ﬁlling phase, and the atrial systole phase, respectively.

3.

Results and discussion

3.1 Eﬀectiveness of the proposed features for
identiﬁcation

Figure 5 shows the B-mode image and color mapping imagesof each of the three features for two typical phases during a
cardiac cycle. The average cross-correlations, CRF,ave ði; j; nÞof RF signals and Cenv,ave ði; j; nÞ of envelopes between
consecutive frames, and the average spatial standard deviation SDave ði; j; nÞ between movement vectors mostly havelarge and small values, respectively, in the area with highechogenicity but mostly have small and large values,
respectively, in the area with low echogenicity. These results
show the eﬀectiveness of the proposed features for identiﬁcation of the heart wall and the chamber. However, in thecolor mapping images of these three features, the blue=purple
areas, i.e., the areas with low cross-correlation value or highdeviation value, are shown in the heart wall. In the color
mapping of CRF,ave ði; j; nÞ and Cenv,ave ði; j; nÞ, the green=
yellow areas, i.e., the areas with high cross-correlation value,
are shown in the chamber. The former areas are caused by
the change in thickness of the heart wall, and the latter areas
are caused by artifacts, which cannot be removed by MTI
ﬁltering. Also in the B-mode images, areas with low and highechogenicity are seen in the heart wall and the chamber,respectively. The inﬂuence of these areas on the identiﬁcation
is evaluated quantitatively in the next section.
Furthermore, the valves in color mapping are not as sharp
as those in B-mode images. This would be caused by error intracking of the valves. In the present study, the radius of thesearch area was set at 595 µm to track the heart wall in theconsecutive frames. It is diﬃcult to track the valves because

the velocity of the valve is much larger than that of the heartwall. However, as shown in Fig. 5, since the valve is
suﬃciently clear in the B-mode image, it is not considered to
be a subject for identiﬁcation in the present study.
Figure 6 shows the temporal changes of features during a
cardiac cycle in three areas, the deﬁnite and indeﬁnite areasof the IVS, i.e., IVS with high and low echogenicity, andthe areas of the LV. Periods A, B, C, D, E, and F denotethe isovolumetric contraction phase, the ejection phase, theisovolumetric relaxation phase, the rapid ﬁlling phase, theslow ﬁlling phase and the atrial systole phase, respectively.
The echogenicity of the indeﬁnite areas of the IVS was close
to that of the LV during the latter half of period B to E. On
the other hand, the average cross-correlations CRF,ave ði; j; nÞof RF signals and Cenv,ave ði; j; nÞ of envelopes and the average
spatial standard deviation SDave ði; j; nÞ of the movement
vector of the indeﬁnite areas of the IVS were close to those of
the LV only during the period from the latter half of period B
to the former half of the period D. These results show theeﬀectiveness of the proposed features in distinguishingindeﬁnite areas of the IVS from LV, and also show thepossibility of more accurate identiﬁcation of the heart walland the chamber than obtainable with the echogenicity.
3.2 Identiﬁcation results using proposed features
Figure 7 shows the temporal change of criterion J ofseparability at the time of identiﬁcation by using echogenicity, the average cross-correlation of RF signals, theaverage cross-correlation of envelopes, and the average
spatial standard deviation of the movement vectors. Table I
shows the mean and the standard deviation during a cardiac
cycle. The identiﬁcation result using the average spatial
standard deviation of movement vectors achieved the best

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K. Takahashi et al.

(a)

(b)

(c)

(d)

Fig. 6. (Color online) Temporal changes of features in three areas. (a) Echogenicity. (b) Average cross-correlation of RF signals. (c) Average crosscorrelation of envelopes. (d) Average spatial standard deviation of movement vectors. Red, green, and blue lines denote the deﬁnite areas of the IVS, indeﬁnite
areas of the IVS, and the LV, respectively. Periods A, B, C, D, E, and F denote the isovolumetric contraction phase, the ejection phase, the isovolumetricrelaxation phase, the rapid ﬁlling phase, the slow ﬁlling phase, and the atrial systole phase, respectively.
Table I. Criterion J of separability during a cardiac cycle, evaluated for(i) echogenicity, (ii) the average cross-correlation of RF signals, (iii) the
average cross-correlation of envelopes, and (iv) the average spatial standard
deviation of movement vectors.

Fig. 7. (Color online) Temporal changes of criterion J of separability.
Results of identiﬁcation using (i) echogenicity, (ii) average cross-correlationof RF signals, (iii) average cross-correlation of envelopes, and (iv) average
spatial standard deviation of movement vectors. Periods A, B, C, D, E, and F
denote the isovolumetric contraction phase, the ejection phase, theisovolumetric relaxation phase, the rapid ﬁlling phase, the slow ﬁlling phase,and the atrial systole phase, respectively.

performance, i.e., J = 3.02 ± 2.27, and the result using
cross-correlation of RF signals and envelopes achieved acomparable performance of J = 1.69 ± 0.842 and 1.40 ±0.577. Particularly during the whole periods A, C, E and F,
criterion J of separability using the proposed features washigher than that using echogenicity, which the conventional
identiﬁcation method was based on. As described in theprevious section, in the color mapping images of Fig. 5,
blue=purple and green=yellow areas are respectively seen in
the heart wall and the chamber, and in the B-mode images,
areas with low and high echogenicity are respectively seen

(i)

(ii)

(iii)

(iv)

0.979 ± 0.276

1.69 ± 0.842

1.40 ± 0.577

2.16 ± 0.455

in the heart wall and chamber. However, by quantitativeevaluation using criterion J of separability as describedabove, it is shown that the proposed three features have asmaller inﬂuence on accurate identiﬁcation than the echogenicity. Since criterion J of separability reﬂects the classiﬁcation accuracy, the feature with high value of J canpossibly enable accurate identiﬁcation, comparable to manual
identiﬁcation by examiner. Therefore, the results show theeﬀectiveness of identiﬁcation using the proposed features.
However, temporal changes of criterion J of separability
using the proposed features are larger than that using
echogenicity, and criterion J of separability using the
proposed features is smaller than that using echogenicity
during the ﬁrst half of period B. This would be caused by the
temporal changes of the proposed features. In order toachieve more stable identiﬁcation during a cardiac cycle, it isnecessary to develop features with low temporal change by
optimization of the parameters of the calculated features, i.e.,
the radius of the small region and the number of frames. In
addition, in order to show the possibility of clinical usage, itis necessary to conﬁrm the eﬃciency of the proposed method
by applying it to more test subjects.
4.

Conclusions

In the present study, we focused on the relative temporalchanges of scatterer spatial distribution and proposed

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eﬀective features for identiﬁcation of the heart wall andchamber. The identiﬁcation results using the proposedfeatures achieved criteria J of separability 1.69, 1.40, and3.02 compared with the result of 0.979 using echogenicity.
The results show the high potential of the proposed features
in identifying the heart wall and the chamber.

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