IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control , vol. 59, no. 11, November 2012

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CorrespondenceHigh-Frame-Rate Echocardiography
With Reduced Sidelobe Level
Hideyuki Hasegawa and Hiroshi Kanai
Abstract—Echocardiography has become an indispensable
modality for diagnosis of the heart. It enables observation of
the shape of the heart and estimation of global heart function
based on B-mode and M-mode imaging. Methods for echocardiographic estimation of myocardial strain and strain rate havealso been developed to evaluate regional heart function. Furthermore, it has been recently shown that echocardiographic
measurements of transmural transition of myocardial contraction/relaxation and propagation of vibration caused by closureof the heart valve would be useful for evaluation of myocardial
function and viscoelasticity. However, such measurements require a frame rate (typically >200 Hz) much higher than that
achieved by conventional ultrasonic diagnostic equipment. We
have recently realized a high frame rate of about 300 Hz witha full field of view of 90° using diverging transmit beams andparallel receive beamforming. Although high-frame-rate imaging was made possible by this method, the side lobe level was
slightly larger than that of the conventional method. To reduce the side lobe level, phase coherence imaging has recently
been developed. Using this method, the spatial resolution is
improved and the side lobe level is also reduced. However,speckle-like echoes, for example, echoes from the inside of theheart wall, are also suppressed. In the present study, a method
for reducing the side lobe level while preserving speckle-likeechoes was developed. The side lobe level was evaluated using a wire phantom. The side lobe level of the high-frame-rate
imaging using unfocused diverging beams was improved by
13.3 dB by the proposed method. In in vivo measurements, a
B-mode image of the heart of a 23-year-old healthy male could
be obtained while preserving the speckle pattern in the heart
wall at a frame rate of 316 Hz with a full field of view of 90°.

I. Introduction

Echocardiography is a predominant modality for
diagnosis of the heart because it provides a crosssectional image of the heart noninvasively in real time.
Because of the high temporal resolution of ultrasonic diagnostic equipment, global heart function, such as ejection fraction (EF), can be estimated based on B-mode
and M-mode imaging much more easily than with otherdiagnostic modalities, such as magnetic resonance imaging(MRI) and computed tomography (CT). It has recently
been shown that ultrasonic measurements of transmuraltransition of myocardial contraction/relaxation and its
propagation [1], [2] and propagation of vibration causedby closure of a heart valve would be useful for evaluationof myocardial function and viscoelasticity [3], [4]. HowManuscript received December 20, 2011; accepted July 20, 2012.
The authors are with the Graduate School of Biomedical Engineeringand the Graduate School of Engineering, Tohoku University, Sendai,
Japan (e-mail: hasegawa@ecei.tohoku.ac.jp).
DOI http://dx.doi.org/10.1109/TUFFC.2012.2490

ever, such measurements require a frame rate much higher
than that achieved by conventional ultrasonic diagnostic
equipment. For example, electrical excitation propagatesin Purkinje fibers and ventricular muscle at typical velocities of 0.3 to 4 m/s [5], and the corresponding propagation
velocities of myocardial contraction of 0.5 to 7 m/s havebeen measured by ultrasound [4], [6]. In these studies,a high frame rate (typically higher than 400 Hz with aslightly reduced lateral field of view, which is much higher
than that realized by conventional ultrasonic diagnostic
equipment, usually several tens of hertz) is required tomeasure the propagation of this electromechanical wave
and the resulting transient small motion of the heart wall.
Konofagou et al. [7] and D’hooge et al. [8] increased theframe rate to above 200 Hz in the ultrasonic measurementof the heart function. However, the size of the field of viewand the total number of scan lines in an ultrasonic image
were significantly reduced.
To achieve a high frame rate, we used sparse sector
scanning, in which the number of scan lines was decreased
to about 10 [9], and applied it to various applications [1]–[4]. In this method, the angle intervals between scan lines
are increased to obtain a large lateral field of view with asmall number of scan lines. Therefore, the lateral image
resolution is significantly degraded.
The aforementioned methods are based on conventional
beamforming; therefore, the density of scan lines or fieldof view must be sacrificed to achieve a high frame rate.
To overcome this problem, parallel receive beamforming[10] with a wide transmit beam has been developed toilluminate a wider region by one transmission to reduce
the number of transmissions. Lu and colleagues proposed
an imaging method using an unfocused but nondiverging
transmit beam, namely, a limited diffraction beam [11]–[14]. Unfocused beams achieved a wider beam width, andnondiverging beams used in these cited studies prevented
the insonified energy from being spread to ensure thatthe required penetration depth was achieved. However,
the width of a nondiverging beam is limited by the size ofthe aperture, which would limit the number of receiving
beams created by one transmission.
High-frame-rate echocardiography at about 300 Hz
with a full field of view of 90° using steered diverging
transmit beams and parallel receive beamforming has recently been realized [15]. Diverging waves were produced
using all transducer elements in an ultrasonic array probe
to obtain ultrasonic echoes with a better SNR [16], [17]than the spherical wave produced by a single element [18].
Although just the idea of a diverging beam produced frommultiple elements was shown in [17], the feasibility of thediverging beam had not been examined. The diverging
beam from multiple elements was shown to be feasible
in high-frame-rate echocardiography [15]. Although highframe-rate imaging is possible by our method, the side lobe

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IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control , vol. 59, no. 11, November 2012

level is slightly larger than that of conventional beamforming. To reduce the side lobe level, phase coherence imaging
has recently been developed [19]. This method sensitively
suppresses echoes influenced by the diversity of phases of
echoes received by transducer elements because of various
factors, such as focusing error, etc. Therefore, the spatial
resolution is improved and the side lobe level is suppressedby this method, but weak speckle-like echoes, which are
generated by interference of scattered echoes, are also significantly suppressed because the phases of echoes would
be influenced by the interference. In the present study,
a method to reduce the side lobe level while preserving
speckle-like echoes was developed. The side lobe level was
evaluated using a wire phantom, and a B-mode image ofa heart of a 23-year-old healthy male was obtained in vivo
by the proposed method.

Using an unfocused wide transmit beam increases theside lobe level compared with conventional beamforming(focusing both in transmit and receive). Therefore, methods for reduction of the side lobe level are required.
When receive focusing is performed with respect to a
spatial point p, the position of the source of an echo does
not always exactly coincide with p. Let us consider thedifference between the time delay applied by a receive
beamformer and the propagation time delay of the echo.
As shown in Fig. 1(a), the locations of focus and thesource of the echo are defined by (x, z) and (x + Δx, z +Δz), respectively. Under such conditions, distance ri′ fromthe ith element to the source and distance ri from the ithelement to the focal point are expressed as(x − x i + ∆x )2 + (z + ∆z )2,(1)(x − x i )2 + z 2,

(2)

ri =

∆ri
c0
≈ ax i + b,

∆τ i =(6)

where c0 is the speed of sound. Constants a and b are
given bya =b=

II. Principles

ri′ =where 2ri + Δri is approximated by 2ri because Δri is assumed to be sufficiently smaller than 2ri.
For large z, distance ri can be approximated to be (x2+ z2)1/2 because xi is limited by the aperture size (xi wasless than 10 mm in the present study). Therefore, residual
time delay Δτi is expressed as∆x
c0 x 2 + z 2,∆x ⋅ x + ∆z ⋅ z
c0 x 2 + z 2

(7)
.

(8)

Residual time delay Δτi is also expressed as the residual
phase delay Δθi :where xi is the lateral position of the ith element.
Residual time delay Δτi (focusing error) of the echo
from the source received by the ith element after receive
beamforming (applying time delay TRBF,i) depends on the
difference between ri and ri′.
(ri′)2 − ri2 = ∆ri(2ri + ∆ri )		
= (x − x i + ∆x )2 + (z + ∆z )2 − (x − x i )2 − z 2,
		(3)
where Δri is ri′ − ri.
By assuming that the focal depth z is sufficiently large,
squares of Δx and Δz can be neglected:∆ri(2ri + ∆ri ) ≈ 2∆x(x − x i ) + 2∆z ⋅ z,
2∆x(x − x i ) + 2∆z ⋅ z
2ri + ∆ri
∆x(x − x i ) + ∆z ⋅ z
≈
,
ri

∆ri =

(4)
(5)
Fig. 1. Illustration of mismatch between the location of a focal point
and that of the source of an echo (a) in receive and (b) in transmission.

hasegawa and kanai: high-frame-rate echocardiography with reduced sidelobe level∆θi = 2π f 0∆τ i,(9)where f0 is the center frequency of ultrasound. In the present study, a method was proposed for reduction of theside lobe level while keeping the shape of the point spreadfunction similar to those in conventional beamforming andour proposed method using diverging beams. As shownin (6), there is a linear relationship between the residual
phase delay Δθi and the lateral position xi of an element
when the location of a focal point is close to that of ascatterer. This means that the difference between residual
phase delays of two neighboring elements is consistentacross the array when the focusing is done near the sourceof an echo (when Δx and Δz are small). This consistency
can be evaluated by the magnitude-squared coherencefunction (MSCF) γ [20], defined as:
L −2

2∑ S i* ⋅ S i +1
γ = L −2 i = 0 2 L −2,2
∑i = 0 S i ∑i = 0 S i +1

(10)where L is the number of elements. The numerator in (10)corresponds to the cross-spectrum between Si and Si+1
averaged across the array. Therefore, the MSCF becomes
1 when the transfer function from Si to Si+1 is constantacross the array. On the other hand, the magnitude of thenumerator decreases because of the incoherent averagingof the transfer function when the transfer function is notconstant. The phase of the transfer function corresponds
to the phase difference between two neighboring elements.
Therefore, the MSCF would decrease when the phase difference between two neighboring elements is not constant[= nonlinear according to the element number (position)].
To obtain the MSCF γ, the complex Fourier coefficient
S ′i at f0 (= 3.75 MHz) of the RF echo signal si(t − TRBF,i)
received by the ith transducer element must be estimated.
To obtain the complex Fourier coefficient S ′i, in the present study, the discrete Fourier transform at f0 was applied
to si(t − TRBF,i) with a Hann window whose length was
0.53 μs. Under this condition, the first nulls of the power
spectrum of the Hann window were located at 0 and
7.5 MHz, providing the available maximum bandwidth of
the resultant complex signal Si sampled at 30 MHz.
The Fourier transform was applied to the RF echo si(t− TRBF,i) received by the ith transducer element after thetime shift by the receiving beamformer to account for thedifferences among propagation time delays of echoes received by transducer elements. However, the time delay
TRBF,i is an integral multiple of the sampling interval of
the RF echo. To remove the residual time delay resulting
from the difference between the actual time delay Δτi andTRBF,i, S ′i is multiplied by exp{2π f0(Δτi − TRBF,i)} to obtain the corrected Fourier coefficient Si in (10). Therefore,
there are no phase differences among corrected Fourier
coefficients {Si} when the location of the source of the echo
exactly coincides with the focal point p [the relationshipbetween residual time delay and an element’s lateral position is linear, but both a and b in (6) are zero]. In this2571

case, the MSCF γ is 1. In addition, according to (6) and(9), there is a linear relationship between the phase delayΔθi = ∠S i and the lateral position xi of the transducer
element when the focal point is located very near thesource of the echoes (small Δx and Δz). In such cases, theMSCF γ is also close to 1 because the phase difference
between the spectra of the signals received by ith and (i +1)th elements is consistent across the array. On the other
hand, the MSCF γ decreases when there is a mismatch
between the locations of the source of an echo and the focal point, (e.g., echoes caused by side lobes) because theassumption of (4) is not applicable. Therefore, such undesirable echoes can be suppressed by weighting the beamformed RF signal at p using the MSCF γ.
Furthermore, the difference between transmit beams inconventional and proposed beamforming is considered toaffect the side lobe reduction. In conventional beamforming, the geometrical center (center of the aperture) is same
in both transmit and receive, as illustrated in Fig. 1(b).
Therefore, the time required for the propagation of ultrasound from the aperture to a scatterer (in transmit) andthat from the scatterer to the aperture (in receive) are
same, and an echo from a scatterer, which is located at
the range distance along the side lobe that is same as therange distance of the focal point, would contribute to thecalculation of the MSCF at the spatial point p = (x, z).
On the other hand, the time required for the propagation from the aperture to the scatterer and that from thescatterer to the aperture are different in our beamforming
using diverging beams because the geometrical center of
the transmit beam is the position of a virtual source of adiverging beam. The time required for the propagation of
a diverging beam from the aperture to a scatterer can be
estimated correctly when the scatterer is located at the
focal point. However, there is an arrival-time estimation
error Δrt, which reduces the contribution of the echo fromthe scatterer to the calculation of the MSCF at the spatial
point p (there is no echo signal in beamforming at p whenΔrt is larger than the pulse duration of ultrasound) when
the scatterer is not at the focal point. Such arrival-time
estimation error would also reduce the coherence of thereceived signals.
III. Evaluation of Spatial Resolution
and Side Lobe Level Using a Wire Phantom
In the present study, a commercial diagnostic ultrasonic system (α-10, Aloka, Tokyo, Japan) was used witha 3.75-MHz phased array probe. The phased array wascomposed of L = 96 elements at intervals of 0.2 mm. The
elevation focal distance was fixed to be 70 mm. This system was modified so that all of the 96 elements can be
excited simultaneously and RF echoes received by L =96 individual elements could be acquired at a sampling
frequency of 30 MHz and a 16-bit resolution for off-line
processing (receive beamforming, compounding, etc.). In
conventional beamforming, receive focusing was done with

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IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control , vol. 59, no. 11, November 2012

respect to each discrete spatial point. The beamforming
procedure in our high-frame-rate imaging is described in[15]. The Hann apodization was used for both conventional beamforming and our high-frame-rate imaging. In
the beamforming procedure, a constant speed of sound of1540 m/s was assumed.
In the basic experiment, fine nylon wires (diameter≈100 μm) placed in water were used for evaluation of
the spatial resolution. Figs. 2(a)–2(d) show B-mode images of the wires obtained by conventional beamforming
and parallel beamforming with diverging beams at rf =100 mm without weighting, with weighting by the MSCF,
and with weighting by the phase coherence factor [19],respectively, where rf is the distance between the front
surface of the array and the virtual point source behind
the array for producing a diverging beam. The dynamic
ranges of Figs. 2(a)–2(d) are 60 dB. For diverging beams,
distance rf was set at 100 mm. In Fig. 2, there is not muchdifference between the B-mode image obtained by conventional beamforming [Fig. 2(a)] and those obtained using
diverging beams with [Fig. 2(b)] and without [Fig. 2(c)]weighting by the MSCF. The B-mode image obtained using diverging beams with weighting by the phase coherence factor [Fig. 2(d)] shows a significantly improved spatial resolution compared with the other images. In Fig.
2(d), the phase coherence factor is obtained as max[0,1− σ/σ0] [19], where σ is the standard deviation of phasesof echoes received by individual elements and σ0 = π /30.5.
The standard deviation σ was evaluated after applying
time delays by the receiving beamformer.
Fig. 3 shows the lateral profiles of the images [corresponding to point spread functions (PSF)] at the shallowest wire. The half-full-widths at half-maxima of the point
spread functions shown in Fig. 3 are provided in Table I.
From the data shown in Fig. 3, the average side lobe levels
were evaluated in the lateral angular ranges, −45° < (lateral angle) < −15° and 15° < (lateral angle) < 45°. The
side lobe level obtained using diverging beams increasedby 8.5 dB compared with conventional beamforming. By
weighting with the MSCF, the side lobe level in the highframe-rate imaging using diverging beams was reduced by
13.3 dB. Weighting by the phase coherence factor showed
the best spatial resolution and the lowest side lobe level inthe phantom experiment.
IV. In Vivo Imaging of a Human Heart
Figs. 4(a)–4(d) show B-mode images of the heart of a23-year-old healthy male obtained by conventional beamforming and parallel beamforming with diverging waves
at rf = 100 without weighting, with weighting by the
MSCF, and with weighting by the phase coherence factor, respectively. Fig. 5 shows the intensity profiles along
the scan lines indicated by the white lines in Fig. 4. Notethat the position of the posterior wall in the measurement with conventional beamforming was slightly shallower than that in the measurement with diverging beams.

Fig. 2. B-mode images of fine wires obtained (a) by conventional sector
scanning, (b) using a diverging beam, (c) using a diverging beam withweighting by the magnitude-squared coherence function (MSCF), and(d) using a diverging beam with phase coherence factor weighting [19].

Using diverging waves [Fig. 4(b)], a B-mode image of theheart could be obtained at a high frame rate of 316 Hz
with a full lateral field of view of 90°. By weighting with
the MSCF [Fig. 4(c)], the image contrast was improved,and speckle-like echoes, for example, echoes in the heartwall, were well preserved. It can be also observed in Fig.
5 that the proposed method using the MSCF suppresses
the undesirable echoes in the cardiac lumen while keep-hasegawa and kanai: high-frame-rate echocardiography with reduced sidelobe level

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TABLE I. Half-Full-Widths at Half-Maxima of Point Spread Functions Shown in Fig. 3.

Width of lateral PSF [mm]Conventional
beamforming
0.66

ing the echoes inside the heart walls. On the other hand,by weighting with the phase coherence factor [Fig. 4(d)],speckle-like echoes inside the heart walls were significantly
suppressed, although echoes resulting from specular reflection, such as an echo from the epicardium, were significantly enhanced. As shown in Fig. 3, although the spatial
resolution is significantly improved by weighting with thephase coherence factor, this characteristic, i.e., significant
suppression of speckle-like echoes, may not be preferable
for analyzing the heart wall, such as estimation of velocity
and strain rate of the heart wall.
V. Discussion
Recently, we have developed a method based on parallel beamforming with diverging transmit beams for highframe-rate echocardiography. To realize B-mode imaging
in a sector format based on parallel beamforming, spherically diverging waves were used in transmission. However,in this method, the side lobe level slightly increased compared with that of conventional beamforming because of
the use of unfocused transmit beams. In the present study,
a method for reduction of side lobe level was developed torealize a side lobe level lower than that of conventional

Fig. 3. Point spread functions in the lateral direction obtained by conventional sector scanning, diverging beam, diverging beam with weighting by the magnitude-squared coherence function (MSCF), and diverging
beam with phase coherence factor weighting [19].

Diverging

Diverging with
MSCF

Divergingphasecoherence

0.82

0.81

0.43

beamforming with a frame rate of over 300 Hz, which ismuch higher than that of conventional beamforming.
To consider small residual time delays of echoes, thephases of the echoes were used in the present study. To
obtain the phase information, the Hilbert transform isused in general. However, the Hilbert transform requires
the Fourier transform of the echo signal and the inverse
Fourier transform of the estimated frequency spectrum.
To increase the computational efficiency, in the present
study, the Fourier coefficient of the echo at only the center
frequency of ultrasound was calculated. This center frequency should be the center frequency of the received RF
echo. However, in the present study, the center frequencyof the ultrasound emitted was used because the estimation of the center frequency of the received echo required
an additional computation. Before calculating the MSCF,
time delays based on conventional focusing were applied
to signals received by individual elements. In this procedure, sub-sample time delays were applied by considering the phase of the echo signal, as described in Section
II. As expressed in (9), the phase delay coinciding withthe corresponding time delay is expressed using the center
frequency of the received echo. Therefore, there would be
errors in application of time delays. However, such errors
are negligible because the errors are smaller than the sampling interval of 25 ns.
In the results of imaging of wires, it was found that theside lobe reduction by the proposed method was depth-dependent, i.e., the side lobe reduction is smaller in a deeper
region than a shallower region, because the change in the
distance from a scatterer to an element caused by the lateral position of the element is smaller in a deeper region.
As suggested for the phase coherence factor [19], the side
lobe reduction can be controlled by taking γα (γ: MSCF),
where α is a variable coefficient. Therefore, in our future
work, it may be effective to control the weights by considering the depth-dependent characteristic of the MSCF γ.
To suppress the side lobe level, the phase coherence factor [19] was recently introduced. This method suppresses
a beamformed echo signal whose standard deviation ofphases of echoes received by transducer elements is large.
Using this method, weak speckle-like echoes are also suppressed because the standard deviation of phases of echoes
received by individual elements would be increased by interference of echoes, which is the source of speckle-likeechoes. In some cases, it is important to observe speckle
patterns of tissues. Therefore, a method for reduction of
the side lobe level with preservation of speckle-like echoes
was developed in the present study. On the other hand,the phase coherence factor improves spatial resolution and2574

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control , vol. 59, no. 11, November 2012

Fig. 5. Intensity profiles along the scan lines indicated by the white lines
in Fig. 4.

of transmit beams, estimation of wavefronts of transmit
beams, etc., are necessary to further improve the frame
rate, such methods for reducing the side lobe level would
be necessary for high-frame-rate imaging to obtain an image contrast comparable to or better than that obtainedby conventional beamforming.
VI. Conclusions

Fig. 4. B-mode images of the heart of a 23-year-old healthy male obtained (a) by conventional sector scanning, (b) using a diverging beam,(c) using a diverging beam with weighting by the magnitude-squared
coherence function (MSCF), and (d) using a diverging beam with phasecoherence factor weighting [19].

also well emphasizes specular echoes, such as echoes fromheart valves in Fig. 4(d), and relatively strong scattering
echoes. The method based on the phase coherence factor
and the proposed method are complementary.
In high-frame-rate imaging, it is necessary to use unfocused transmit beams. Therefore, the side lobe level
increases in general. Although optimization of transmit
conditions, such as angular beam width, angular intervals

In this study, a method of suppressing the side lobelevel was developed for high-frame-rate echocardiography
based on parallel beamforming with diverging transmit
beams. To realize suppression of the side lobe level while
preserving speckle-like echoes, the MSCF between echoes
received by individual transducer elements was used forweighting a beamformed RF echo. Using the proposed
method, it was confirmed by basic experiments using finewires that the side lobe level could be reduced by 4.8 dBcompared with conventional beamforming. Furthermore,in in vivo measurements, an ultrasonic image of a heartwith a full field of view of 90° at a frame rate of 316 Hz
could be obtained with an improved image contrast andpreservation of speckle-like echoes.

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