HighH
Framme Rate Echocarrdiography for
Detailed Analysis
Aof Cardiiac Dynaamics
Hideyuki Haseegawa1,2 andd Hiroshi Kanai2,1
1 GraduateG
Schoool of Biomediccal Engineerinng, Tohoku Unniversity
2 GraduateG
Schoool of Engineerring, Tohoku UniversityU
E-m
mail: hasegawaa@ecei.tohokuu.ac.jp, hkanaii@ecei.tohokuu.ac.jp

Abbstract
Echocardioggraphy is a w
widely-used modalitymfordiaagnosis of thee heart. It enaables observattion of theshaape of a heart anda estimationn of global heaart function
bassed on B-modee and M-modee imaging. Sub
bsequently,
meethods for esttimating myoccardial strain and strain
ratee have been developed to evaluate regional heartfunnction. Furtherrmore, it has bbeen recently shown thatmeeasurements of transmural ttransition of myocardialcon
ntraction/relaxxation and prropagation off vibrationcau
used by closurre of a heart vvalve would bee useful forevaaluation of myyocardial funcction and visccoelasticity.
Hoowever, such measurementts require a frame ratemu
uch higher thhan that achhieved by coonventionalultrrasonic diagnoostic equipmennt. In the preseent study, ameethod based ono parallel recceive beamforming wasdevvelopedtoachieevehigh-frame-rateechhocardiographyy over 300 Hzz. To increasee the frame
ratee, the numberr of transmits was reduced to 15 with
ang
gular intervals of 6 degrees,, and 16 receiv
ving beams
were created foor each transsmission to obtain thenummber and denssity of scan liines which weere same asthoose realized byb conventionnal sector sccanning. In
adddition, several transmits werre compoundeed to obtaineacch scan line tot reduce the differences inn transmitrecceive sensitivitties among scan lines. The number oftran
nsmits for compoundingg was deterrmined byconnsidering the width of thhe transmit beam.
b
For
tran
nsmission, plaane waves andd diverging waves
w
were
inv
vestigated. Diverging
Dw
waves showeed better
perrformance thann plane wavees because thee widths ofplaane waves didd not increase with the rang
ge distancefrom an ultrasonnic probe, whereas lateral intervals
iofscaan lines increaased with rannge distance. The
T spatial
resolution of the proposed metthod was valid
dated using
finee nylon wires. Although the widths at haalf maxima
of the point sprread functionss obtained byy diverging
waves were sligghtly larger tthan those ob
btained byconnventional beaamforming annd parallel beeamforming
witth plane wavees, the point spread functio
ons, whichwere very simillar to that obbtained by coonventional
beaamforming could be realized byy parallel
beaamforming witth diverging bbeams and com
mpounding.
Hoowever, there wasw an increase in the laterral sidelobe
lev
vel in the casee of parallel bbeamforming with planeandd diverging waves.
w
Furtherrmore, a hearrt of a 23yeaar-old healthy male was meaasured. Althou
ugh contrastof the B-modeBimage obtained by thhe proposed methodm
was deg
graded due too the increaseed sidelobe leevel, aframe raate of 316 Hz,, which was mmuch higher thaan thatrealized
d by conventional sector scannning of severral tensof Hertzz, was realized with a full lateral field of viewof 90 deegrees.

1. Intro
oduction
Echocardiography is one off the predomminantmodalities for the diagnosis
dof thhe heart becaause it
provides a cross-ssectional imaage of the heart
noninvaasively in real time. Owing tto the high tem
mporalresolutio
on of ultrasonnic diagnosticc equipment, global
heart fu
unction, such as ejection frraction (EF), canc beestimateed based on B-mode andd M-mode im
magingmuch moremeasily comparedcwitth other diaggnostic
modalities, such as magneticmresonaance imaging (MRI)
and com
mputed tomoggraphy (CT). T
To evaluate reegional
myocarddial functionn quantitativvely, method
ds formeasureements of myoocardial strain and strain rate havebeen developed [1-3].. These methods enable estim
mationof regio
onal deformattion of the hheart wall bassed on
measureements of movvement. Although measured
d strainand straain rate themselves are usefful for evaluattion of
the regiional myocarddial function, it has recently
y beenshown thatt
the measuurements of trransmural tran
nsitionof myoocardial contraaction/relaxatioon and propaagationof vibraation caused byb closure of a heart valve would
be usefful for evaluaation of myoccardial functio
on andviscoelaasticity [4-6].. However, ssuch measureements
require a frame rate muchmhigher thhan that achiev
ved byconventtional ultrasoonic diagnostiic equipmentt. For
examplee, electrical excitationeproppagates in Pu
urkinjefibers annd ventricular muscle at typical velocities of 0.3
to 4 m/s
m [7], and the correspoonding propaagation
velocitiees of myocarrdial contractioon of 0.5 to 7 m/s
were measured by ulttrasound [5,8]. A high framme rate,typicallyy higher thann 200 Hz, whhich is much higher
than thaat realized by conventionalcuultrasonic diaggnostic
equipmeent of severaal tens of Heertz, is requirred tomeasuree the propaggation of thiss electromech
hanicalwave annd the resultinng transient ssmall motion of theheart waall.
Kono
ofagou et al. [9] and D
D’hooge et al.[10]increaseed the frame rater
to above 2200 Hz by red
ducingthe sizee of the field of view and the total num
mber ofscan liines in an ultrasonic im
mage. Furtherrmore,
Konofag
gou et al. introduced a electrocardiiogram(ECG)-ggating techniique in ultraasound imagiing tocombine individual small sectors into a large field ofview [11]. In this method, the lateral size of a sector(corresponding to the number of scan lines), which is
obtained in one acquisition, is narrowed to achieve ahigher frame rate of about 500 Hz. By measuring a
number of small sectors during the corresponding
number of cardiac cycles, the measured small sectors
are combined into a large sector format based on ECGgating. Although this method achieves a frame rate ofabout 500 Hz, which is much higher than theconventional frame rate of several tens of Hertz,
measurements for a number of cardiac cycles are
required.
To achieve a high frame rate of about 500 Hz
without ECG-gating, we used sparse sector scanning,in which the number of scan lines was decreased toabout 10 [12]. In this method, the angle intervals
between scan lines are increased to obtain a large
lateral field of view with a small number of scan lines.
Therefore, the lateral image resolution is significantly
degraded.
The above-mentioned methods are based onconventional beamforming. Therefore, they need tosacrifice the density of scan lines or field of view toachieve a high frame rate. To overcome this problem,
parallel receive beamforming with a wide transmit
beam have been developed13) to illuminate a wider
region by one transmission to reduce the number oftransmissions. This could be done in the cited study by
conventional transmit beamforming (focusing at a
certain range distance) because such beams are wide in
the region shallower than the focal distance (between
the transducer surface and the focal point). Using thismethod, real-time 3D imaging of the heart was realized
at a frame rate of a few tens of Hertzes. However, thewidth of the transmit beam is narrower than the size ofan aperture, and this would limit the number ofreceiving beams created by one transmission.
Lu et al. proposed an alternative imaging method
using unfocused but non-diverging transmit beam,
namely, limited diffraction beam [14-17]. Unfocused
beams achieved a wider beam width, and nondiverging beams used in these cited studies prevent theinsonified energy from being spread to assure therequired penetration depth. However, the width of anon-diverging beam is still limited by the size of anaperture.
On the other hand, diverging beams have potential toenlarge the region illuminated by one transmission. In
synthetic aperture ultrasound imaging, a single element
or a small number of elements are used to produce
spherical waves [21,22]. Although a spherical wave
can illuminate a wide area by one transmission,acoustic pressure significantly decreases withpropagation distance, and the signal-to-noise ratio(SNR) of the received signal would be significantly
reduced.
In the present study, the feasibility of a diverging
transmit beam in ultrasonic imaging with parallel
beamforming [18-20] was investigated to achieve aframe rate above 200 Hz with an adequate lateral
spatial resolution, a wider field of view, and no ECG-

gating. Diverging waves can be produced by using alltransducer elements in an ultrasonic array probe toobtain ultrasonic echoes with better SNR.23) The
width of diverging angle was limited to suppress the
decay of acoustic pressure due to the propagation
distance. Furthermore, the diverging beam was steered
to obtain an ultrasonic image of a heart with a fullangle of 90 degrees with a limited beam width. To
increase the frame rate, the number of transmits was
reduced to 15 with a transmit angular interval of 6
degrees, and 16 receiving beams were created in eachtransmit to obtain the number and density of scan lines
which were same as those realized by conventional
sector scanning. The spatial resolution of the proposed
imaging method was evaluated by basic experiments
using fine nylon wires. Furthermore, B-mode images ofa heart of a 23-year-old healthy male measured by the
proposed method were obtained.

2. Materials and Methods
2.1. Mathematical description of ultrasoundwaves emitted from transducer elements
Let us describe ultrasound waves emitted fromtransducer elements of a phased array ultrasonic probe.
To achieve a frame rate over 200 Hz under a typicalpulse repetition frequency of 5 kHz (realized by theultrasound system used in the present study under asetting of an observation range of 130 mm), thenumber of transmits should be less than 25. Therefore,
in the present study, plane waves or diverging waves
were transmitted in 15 directions {mΘ} (m = −7, −6, · ·· , 0, 1, · · · , 7) with angular intervals of Θ = 6 degrees.
The ultrasonic wave gi,m(p; t) at time t from the time oftransmission, which is emitted from the i-th transducer
element (i = 0, 1, · · · , L − 1) in the m-th transmission
and insonifies to a spatial point p = (r, θ), as shown in
Fig. 1, is expressed as follows:
; =
,
(2.1)
− ,,
,
where si(t) is the impulse response of the i-thtransducer element, and τt,i,m(p) is a time delay due topropagation of an ultrasonic wave from the i-th
element to the spatial point p. The time delay τt,i,m(p) of
gi,m(p; t) is given by
∆

=

,,

+

,,

, (2.2)where Δx and c0 are the lateral pitch of transducer
elements and speed of sound, respectively, and TTBF,i isthe time delay applied to the i-th element by thetransmit beamformer.
To emit a plane wave at the steering angle of mΘ,TTBF,i,m should be given by
∙∆ ∙
,,

=

≥ 0,
∙∆ ∙

< 0.
( i = 0, 1, …, L-1)

(2.3)

requiredd to steer the direction of thhe transmit beeam tomΘ. Thhe second termm, which is required to reaalize adiverginng wave, was obtained in tthe present stu
udy byconsidering the geom
metry illustrateed in Fig. 2(bb). Thesecond term dependss on the distannce from the virtual
point soource Ov to thee i-th element iin Fig. 2(b).

Figg. 1. Illustratiions of a plaane wave inso
onifying tospaatial point p = (r, θ) and propagation distance rcoss(mΘ − θ) reequired to illuuminate spatiaal point p,whhich is located at distance r from the centeer of array,usin
ng a plane wavve.
The
T
time delaydTTBF,i,m applied byy transmit
beeamformer is greatergthan orr equal to zero.
For
F a circularr planar transsducer, the Frresnel zone(ran
nge of near fiield) is definedd by the diammeter of theapeerture D and ultrasonicuwaveelength λ as D2/(4λ). The
apeerture width D of the sector probe and thee ultrasonicwavelength λ used in the pressent study werre about 20mm
m and about 0.4
0 mm (centerr frequency: 3.75
3
MHz),
resp
pectively. Althhough the phaased array pro
obe used inthee present studyy was not cirrcular, the ran
nge of near
fielld can be appproximately obtained baseed on thisequuation. The raange of the Frresnel zone off the probe
useed was 250 mm
m and, thus, the range off about 130mm
m, which wass imaged in the present study,s
wasinccluded in the near field. In thhe near field, th
he width ofa planepwave isi constant. O
On the otherr hand, in
ultrrasonic imaginng in a sector format, the laateral widthof a small sectorr imaged by onne transmission increases
witth range distaance and, thuss, the perform
mance of aplaane wave woulld be limited bbecause the laateral widthof a plane wave does not incrrease with rang
ge distancein thet near field.
To
T solve thiss problem, inn the presen
nt study, adivverging wave, which is illustrated in Fig
g. 2(a), wasuseed for transmiission in addittion to a planne wave. In
synnthetic apertuure imaging, each single element is
inddividually useed to emit a spherical wave.
w
Such
div
verging wavees would be useful for ultrasonicimaaging in a secctor format. H
However, the intensity
iofthee emitted wavee would signifficantly decreaase because
a singleselemennt is used. A
Alternatively, sphericallydivverging wavess [22] can be produced using all thetran
nsducer elemments in everry transmissio
on. In thepreesent study, suuch a diverginng wave was realizedrbyapp
plying time delaydTTBF,i,m to the i-th transducer
element in the m--th transmissioon, which is giiven by
,,

=

∙∆ ∙

+
∙∆ ∙

Fig. 2. IllustrationIof a diverging w
wave. (a) Propaagation
distancee r1 required too illuminate sppatial point p, which
is locateed at distance r from the cennter of array, usinguadiverginng wave. (b) GeometryG
for cconsideration ofo timedelays appliedato trannsducer elemeents for transm
missionof diverrging wave.

2.2. Pa
arallel receivve beamformming
In this study, ultraasonic beams (plane or div
verging
waves) emitted in 15 directions an angle intervalls of Θ
= 6 deegrees and 16
1 receiving beams with angle
intervals of 0.375 degrees weree created forr eachtransmitt to realize thee number and ddensity of scann lineswhich area similar too that obtaineed by convenntionalsector scanning.
s
The value, Ôm(p), of the beamfformed
RF signnal at a spaatial point p is generated
d fromultrasonnic echo siggnals {yi,m(t)} received byb theelementts (i = 0, 1, ..., L − 1), whhich contain echoesescattered at all pooints illuminaated by the m-thtransmisssion, as follow
ws:
O

=∑

,

∙

,

,,

< 0,

(2.4)
wh
here rf is the distancedfrom a virtual pointt source Ov
behhind the array to the surfacee of the transd
ducer array.
Thee first term ini the right-haand side of eq.
e (2.4) is, (2.5),,where wr,i (i = 0, 1, · · · , L − 1)) corresponds to thereceive apodization, and τRBF,i,m(pp) is the time delays
be appplied by a receive beamform
mer towhich shouldcompennsate the propaagation delay of the emittedd wavefrom thee probe to p annd that of the scattered wave fromp to thee i-th element. The time dellay τRBF,i,m(p), which
was appplied by the reeceive beamfoormer to echo signal
yi,m(t) reeceived by the i-th element, iis given by

≥ 0,
+

−

=

,

+

∆

.

(2.6)
The seccond term of eq. (2.6) corresponds to the timedelay off a scattered eccho from the sspatial point p to thei-th eleement. The fiirst term, TTW
W,m(p), of eq.. (2.6)
correspo
onds to the propagationpdeelay of the emittedeultrrasonic wave tot spatial pointt p which depeends on therecceiving beam angle θ. Inn the present study, as
illu
ustrated in Figg. 1, for a plaane wave, TTW,m(p) was
asssigned as follow
ws:
,

=

.

(2.7)

Forr diverging waves,w
as illlustrated in Fig. 2(b),TTW
ws:
W,m(p) was assiigned as follow
,

=

,

(2.8)

= sin Θ − sin Θ + sin ,(2.9)= − coss Θ + coos Θ − coos , (2.10)
r = ∙ − 1 ∙ ∆ ∙ sin Θ ,(2.11)
whhere (x, z) is the position of p in thee Cartesiancooordinate.
By
B changing θ ((m−0.5)·ΘΘ ≤ θ < (m++0.5)·Θ) at
inteervals of 0.3775 degrees at each range po
osition r ineacch of the m trransmissions, beamformed RF signals{Ôm(p)} at all sppatial points {pp = (r, θ)} in the field ofvieew are obtainedd.

plane wavewtransmission. As can be seen in Fig.
F
3,
there are significant discontinuitiesdat the edges ofo eachregion imaged by onee transmission..

2.3. Sppatial compoound of multtiple transm
mits inreceivee beamformiing
As describeddin the previous section, therre are
discontiinuities in an ultrasoundu
immage when each scanline is createdcby eacch single transmission becau
use thelateral inntensity profilles of transmitt beams signifiicantly
differ betweenbtransmmissions due to a large angularainterval of transmit beamsb(in general, the inten
nsity isdecreaseed by steeringg due to directtivities of transducer
elementts). Such discoontinuities connsist of high spatial(angularr) frequency components, which degradde theimage quality. A simple wayy to reduce suchdiscontiinuities (high spatial frequeency componennts) inan ultraasound image obtainedoby paarallel beamfo
ormingis to usee spatial movinng average, i.ee., low-pass filtering.
Spatiallyy averaged beeamformed RF
F signal Ôs(r, θ) at a
spatial pointpp = (r, θ)) is expressed as follows:OFigg. 3. Longitudiinal B-mode iimage of a heaart of a 23yeaar-old male obtained by parallel beeamforming
witthout spatial coompounding.

2.3
3. Problem in parallell beamformming withphhased arrayTo
T obtain an ultrasonic immage in a sector format,
ultrrasonic beamss need to be steered. Theerefore, thedireectivity of thee ultrasound bbeam changes dependingon the steering angle. In recceive beamfo
orming, thedifffference betweeen the direcctivities of neighboringnrecceiving beams is not so signnificant becausse the angle
inteervals of receiiving beams arre small (0.37
75 degrees).
Hoowever, such differencedis siignificant in trransmission
beccause of a relatively laarge angle interval ofneiighboring trannsmit beams oof 6 degrees (uused in thepreesent study). ThisT significannt change in diirectivity intran
nsmission prooduce disconntinuities in a resultant
ultrrasonic imagee at a pitchh of 6 degreees, whichcorrresponds to angular intervvals of transmit beams
beccause the trannsmit-receive ddirectivity is defined bythee product of thet transmit aand receive directivitiesd[244]. Figure 3 shhows a B-mode image of thee heart of a
23--year-old heallthy male, whhich was obtaained usingparrallel beam forming
foexpreessed by eq. (2.5) with

,

=

∙O

, +Θ

=

∙O

, +Θ∙

∙ exp − 2Θ∙|,
(2.12)
where thet number off averaging iss expressed byy (2Ms+1), wj is a weighhting function, and m0 is
i thetransmisssion numbeer that givves the min
nimum
differennce between thhe direction oof transmissio
on mΘ
and the direction θ off point p = (r, θθ). As can be seensineq. (2.12), the movinng average opperation corressponds
to the FourierFtransfform with resspect to an angularafrequency fθ of zero.. The spatial frequency speectrum
obtainedd by eq. (2.122) is expressedd by the convo
olutionof the spatialsfrequenncy characterisstics of wj andd Ôm(r,θ) and, thus, the spaatial frequenccy characteristtics of
low-passs filtering byy moving avverage operattion isdeterminned by that ofo the weightinng function wj. It is
well kn
nown that a rectangular weighting fu
unctionexhibitss a higher sidelobeslevell in the freq
quencydomain,, which corressponds to higgher leakage ofo highspatial frequency coomponents. Thherefore, a taapered
functionn, such as a HanningH
winddow, which ex
xhibits
lower sidelobe leveel, is preferaable for weiighting
functionn wj .
Altho
ough the high spatial frequenncy componen
nts canbe reduuced by spatiaal averaging, tthe image wou
uld beblurred because the beamformed RF
F signals {Ôm(p)}(atdifferennt spatial possitions {p} arre averaged in eq.
(2.12). To avoid succh blurring efffect, in the presentpstudy, RFR signals {Ôm(p)} beamforrmed with resp
pect tothe samme spatial posiition p in difffferent transmiissions{m} aree compounded. This proceedure has a similarseffe
fect given by eq.
e (2.12) because the lateral intensity
pro
ofiles of unfoccused beams, such as planee wave anddivverging wave,, are almost homogeneouss at everyanggle θ within thhe beams. Theerefore, we assumed thatÔm0(r, θ +Θ· j) ≈ Ôm0+j(r, θ).

given byy (2Mc + 1)Θ/2 < θw. To saatisfy this con
ndition,the num
mber of com
mpounding w
was determin
ned asfollows:=.
(2.19)(

Fig. 5. Angular widtths {θw} calcuulated for plan
ne anddiverginng waves.
g. 4. Illustration of angular w
width θw of em
mitted wave.
Fig(a) Plane wave. (b)( Diverging w
wave.
By
B replacing thet summationn with respect to angle ineq. (2.12) by thhat with respeect to transm
mission, thecommpounded beamformed RF
F signal Ôc(pp) at p isexppressed as folloows:
=

O

∙

,

,

2.13

wh
here the numbber of compoounding is ex
xpressed as(2M
Mc + 1). In the present studyy, Hanning weiighting was
useed in spatial compoundingg and is exp
pressed asfolllows:
−

Θ

2.14
,
2 1∙ 2 +1 Θ2
whhere the numbber of compoounding is ex
xpressed as(2M
Mc + 1). In thhe present stuudy, Mc was determinedfrom the angullar width of the emitted wave by
connsidering the transducer geeometry, as illlustrated inFig
g. 4. For planee waves, the aangular width θw at range
distance r is giveen by∙∆(2.15)= 2arctaan.
,= coss∙Forr diverging waaves, the diverrging angle φ is obtained
as follows:f
ϕ = arctan∙∆.

(2.16)In the present sttudy, using the diverging an
ngle ϕ, thelateeral beam widthw
lw at range distaance r isapp
proximately giiven by=+ tan .
(2.17)
Thee angular widtth θw for diverrging wave is obtainedoasfolllows:= 2arctaan .
(2.18)(2Mc + 1) is determined
Thee number of compoundingcso that the conntribution off the emissio
ons, whose
direections are diffferent from thhe direction ofo interest θ
by larger than halfhthe anguular beam wid
dth θw, aregraadually decreaased. In the present studyy, this was

In thee present studyy, the angular beam width θw wereintroducced to considder the relatioonship betweeen the
beam widthwand the innterval of trannsmit beams beecause
sparser transmissionss requires a laarger beam wiidth toilluminaate a larger regionr
betweeen the directio
ons ofsuccessiive transmissiions. The anggular beam wiidth ismore convenientcthaan the beam width in diistancebecausee the angular innterval of transmit beams do
oes notchange with the rangee distance, whhereas the interrval indistancee changes. Inn Fig. 5, anngular widths {θw}calculatted for plane and divergingg waves usinng eqs.
(2.15) anda(2.18) arre plotted as functions of range
distancee r (size of apperture L ·Δx = 19.2 mm wasw thesame ass that of the ultrasonic prrobe used). AngularAwidth θw of a diverginng wave at disstance rf of a virtual
point soource larger thhan 100 mm does not channge somuch comparedcwithh that of a pplane wave. At
A thelongest range distannce of 130 m
mm, which was
w ofinterest in the presentt study, angullar width θw doubles
at rf = 100 mm andd triples at rf = 50 mm. AngularA
wever,
width θw would furtheer increase at ssmaller rf. How
the intensity of thee emitted w
wave would furtherfdecreasee. Therefore, in the preseent study, divverging
waves ata rf = 100 mm
m and 50 mm w
were investigaated in
the subssequent sectionns.

3. Resu
ults
3.1. Evvaluation of spatial reesolution usiing awire phhantomIn th
he present study,s
a com
mmercial ultrrasonicdiagnosstic system (αα-10, Aloka, Tokyo, Japann) wasused wiith a 3.75-MHzz phased arrayy probe. This systems
was moodified so thatt RF echoes rreceived by L = 96
individu
ual elements couldcbe acquuired at a sam
mplingfrequency of 30 MHz for off-line processing (rreceive
beamforrming, spatial compoundingg, etc.).
In thee basic experim
ment, fine nyloon wires (diammeter ≈
100 μmm) placed in waterw
were useed for evaluattion of
the spattial resolutionn. Figures 6(aa)-(d) show B-modeBimages of the wires obtained by conventional sector

scaanning and parallel beam
mforming wiith spatialcom
mpounding using plane wavves and diverg
ging waves
at rf = 100 mm anda 50 mm, reespectively. In
n Figs. 6(1)andd 6(2), rectanggular apodization (wr,i = 1; i = 0, 1, 2, ...,
L − 1) and Ham
mming apodizzation (wr,i = 0.54−0.46
coss(2πi/L); i = 0,, 1, 2, ..., L−1)) were respecttively used.
As can be seeen in Fig. 6, the sidelo
obe levels
nificantly inccreased when rectangular apodizationasign
was used. Thereefore, Hamminng apodizationn was usedin thet subsequentt experiments.

7 are described in taable I. As shoown in Fig. 7, plane
wave trransmission achievedathe best lateral spatial
resolutio
on. Although the widths at half maxima of thepoint sppread functionns obtained bby diverging waves
were slightly largger than thhose obtained byconventtional beamforming and paarallel beamfo
ormingwith plane waves, thhe point spreaad functions, which
ntionalwere veery similar too that obtaineed by conven
beamforrming couldd be realiized by parallelpbeamforrming with divverging beamss and compou
unding.
Figures 8(a) and 8(b)) illustrate point spread fun
nctions
created by compoundding plane annd diverging waves,w
respectiively. The wavefronts and point spreadfunctionns shown by thhe dashed and solid lines illu
ustratethose obbtained by thee transmission at the least stteering
angle andathat at thetmaximumm steering ang
gle inbeamforrming with respectr
to sppatial point p.
p Theoverlappping area of tw
wo point spreaad functions in
n Fig. 8
is enhaanced in the resultant poiint spread fu
unctionobtainedd by compounnding. As can bbe seen in Fig.. 8, theoverlappping area obttained by planne waves is smallersthan thaat obtained byy diverging beams, even wh
hen themaximuum steering anngles are sam
me. Therefore, it wasconsidered that planee wave transm
mission achiev
ved thebest lateral spatial reesolution. How
wever, there wasw anincreasee of the laterall sidelobe leveel by use of parallelpbeamforrming with bothbplane annd diverging waves.
w
Althoug
gh this increaase of the siddelobe level would
degradee the imagee contrast, tthe lateral spatial
resolutio
on comparablle to that of conventional sector
scan waas achieved byy the proposed method.

Fig
g. 6. B-mode images of finne wires obtaiined by (a)connventional secttor scanning aand parallel beeamformingusinng (b) plane waves,w(c) diverging waves at rf = 100mmm, and (d) diiverging wavees at rf = 50
0 mm. (1)Recctangular and (2) Hamming apodizations were
w used.

Fig. 7. Axial and laterallprofilees of envelop
pes ofbeamforrmed RF echoeseobtainned by resp
pectivemethodss. (a) Axial prrofile at a lateeral angular po
ositionof 0 deggrees. (b) Lateeral profile at a range distaance of
41 mm.

InI
the B-mmode image obtained byy parallel
beaamforming withw
plane waaves, the pooint spreadfunnction at a largger steering angle (surroundeed by whitedasshed lines in Fig.
F 6(2-b)) w
was distorted (split in thelateeral direction)) because the widths of pllane waves
were narrow com
mpared with ddiverging wav
ves and thewiddths decreaseed when the steering angleawasinccreased. Thereffore, the use oof plane waves is limited
to imaging at sm
maller steerinng angles. On
n the otherhannd, such distoortion was noot found in thhe B-mode
imaages obtained by paralllel beamformming with
div
verging waves..
FiguresF7(a) and 7(b) show the axial and lateral
pro
ofiles of the immages (corressponding to pooint spreadfunnctions) at an angular posittion θ of 0 degrees
d
and
ran
nge distance r of 41 mm, resspectively. Th
he widths at
hallf maxima of thhe point spreaad functions shhown in Fig.

Fig. 8. WavefrontsW
annd point spreadd functions pro
oducedby (a) planepwaves annd (b) diverginng waves.

Tab
ble 1. Widthhs at half mmaxima of po
oint spreadfunnctions shown in Fig. 7.
In
I Fig. 7, the numbernof commpounding (2M
Mc + 1) was
dettermined by eqq. (2.19). In Fiig. 9(1) and 9((2), Mc wasalso
o determined by eq. (2.19),, however, thee maximumof Mc was limitted to be 4 aand 2, respecctively. For
divverging waves,, B-mode imaages obtained byb limiting
thee maximum numbernof coompounding werew
betterthaan those obtainned with unlim
mited Mc, as sho
own in Fig.
6. In the presennt study, the ppropagation deelay of theemmitted wave waas calculated based on eq. (22.8) without
connsidering the distortion of wavefront duue to beam
steeering. Thereffore, it can bbe considered
d that thenummber of compounding Mc larger than 2(coorresponding too larger differeences among thet steeringanggles in emissions used for compoundingg) degradedthee resultant imaages because it would be difficult toestiimate propagaation delays at larger steeringg angles byeq. (2.8) and the large numberr of transmissio
ons (meansa laarge differencce among the angles of tran
nsmissions)
useed for compouunding degradees coherent com
mpounding.
As in Fig. 7, Fig.. 10 shows lateeral profiles off envelopesof compounded beamformed RF echoes at a range
distance of 41 mm
m obtained byy a diverging beamb
at rf =
50 mm with andd without limittation of Mc ≤ 2. In Fig.
10,, only the proffiles obtained w
with a diverging beam at
rf = 50 mm area shown bbecause the number
nofcom
mpounding is largest amongg the transmit beamsb
usedin thet present stuudy. As shownn in Fig. 10, degradationdof coherent coompounding reduces the difference
bettween the mainn lobe and sideelobe levels an
nd does not
imp
prove the spaatial resolutionn. Consequen
ntly, in thepreesent study, thhe number of compounding (2Mc + 1)
was determined by eq. (2.19);; however, itss maximum
was restricted to be 5 for divergging waves.
In
I general, thee insonified energy of a diverging wave
sprreads and acousticainteensity decreaases withpro
opagation disttance. To redduce this deccay, in thepreesent study, thhe width of tthe diverging beam waslim
mited. Figure 11 shows thhe axial profiiles of theultrrasound imagees of the wire phantom (shoown in Fig.
6) at a lateral angleaof 0 deegrees. As exp
pected, thengest wheninteensity at thee deepest wirre was stronfoccusing was doone in both ttransmit and receive, as
sho
own in Fig. 11.
1 Although the intensity was lower
thaan that obtained by focusinng in both traansmit andrecceive, the diveerging waves uused in the preesent study
achhieved decays of intensitiess (Figs. 11(c) and 11(d))
whhich were simillar to that realized by plane waves (Fig.
11((b)).

Fig. 9. B-mode imaages of fine wires obtainned byparallel beamforminng with (a) plane waves, (b)diverginng waves at rf
r = 100 mm
m, and (c) div
verging
waves at rf = 50 mm.
m
Maxima of the numbber ofcompouunding were lim
mited to be (1)) 4 and (2) 2.

Fig. 10. Lateral profi
files of enveloopes of beamfformed
RF echooes at a range distance of 41 mm obtaineed by adiverginng beam at rf = 50 mm
m with and withoutw
limitatio
on of Mc ≤ 2.

3.2 In Vivo Imagin
ng of a Humaan Heart
Figurre 12(a)-(d) shhows B-mode images of thee heartof a 23--year-old healtthy male obtained by convenntionalsector scan and paralllel beamforminng with plane waves
and div
verging wavess at rf = 50 mm and 100
0 mm,
respectiively. The maximumm
off the numbber ofcompouunding Mc wass limited to 2 ffor diverging waves.
w
Althoug
gh a B-mode im
mage of a heaart could be ob
btainedby planne wave transm
mission, the pooint spread fu
unctionproduceed by parallell beamformingg with plane waves
were spplit in the lateral direction, as shown in Fig.
F 6.
Therefoore, it might be better too use plane wave
transmisssion with a smallers
maxim
mum steering angle.
By usinng diverging waves,w
as show
wn in Figs. 12((c) and12(d), B-modeBimages of the heart could be obtaiined at
a high frame
frate of 316
3 Hz with a full lateral fieldfiofview off 90 degrees, anda the divergiing waves at rf = 50

mmm and 100 mm showed similar perrformances.
Altthough the image contrast w
were degradedd due to thehiggher lateral siddelobe levels, a B-mode imaage, whose
imaage quality was
w comparabble to that ob
btained byconnventional secctor scanning, could be obttained at afram
me rate (316 Hz) significanntly higher thaan that (39Hz) obtained byy conventionall sector scan, and a fullo 90 degreess was achieveed without
fielld of view ofreqquiring ECG gaating [11].

In addittion, phase abberration correction [26,27] would
be usefu
ul for receive beamforming.
bg. 11. Axial proofiles of the immages of wiress (shown inFig
Figg. 6) at a lateraal angle of 0 ddegrees. (a) Co
onventional
beaamforming (foocusing in botth transmit annd receive).
(b) Parallel beam
mforming with plane waves. (c) and (d)Parrallel beamformming with divverging beams at rf = 100mmm and 50 mm, respectively.

4. Discussion
DIn
I the present study, a meethod based on parallel
beaamforming was investigateed for high frame rateechhocardiographyy. To realizee B-mode imaaging in a
secctor format based on parallel beaamforming,sphherically divergging waves weere used in transmission.
In
I the presentt study, in reeceive beamfo
orming, theproopagation delaay of the emittted diverging
g wave wascalculated by considering the geometrry of thetran
nsducer array and the virtuaal point sourcee. However,thee increase of thhe number of ccompounding Mc, whichcorrresponds to thhe increase of the transmissiion steeringang
gle from the direction of iinterest θ, deegraded theresuultant B-modee images. Thiss would be cau
used by the
distortion of the wavefront of the emitted wavew
due tosteeering. In fuuture work, methods forr accurate
reaalization of thetdesired wavefront or accurate
calculation of thee resultant wavvefront will bee necessary
to increase the number of compounding for further
imp
provements ofo the image resolution because thedifffference in angles
aof w
wavefronts inn different
trannsmissions woould increase bby using moree number oftran
nsmissions forr compoundingg, as illustrated in Fig. 8.

Fig. 12. B-mode imaages of a heaart of a 23-yeear-old
healthy male obtainned by (a) cconventional sector
scanning and paralleel beamforminng using (b) planewaves, (c) diverging waves at rf = 100 mm, and (d)ng waves at rf = 50 mm. Thhe maximum numberndiverginof commpounding was limited to be 2 for div
verging
waves.

AlthoughA
diveerging waves sshould be used
d to achievea fullfu lateral field of view of 90 degrees, pllane waves
cou
uld be used foor imaging of a narrower reg
gion. Plane
waves are morre easily impplemented in ultrasonicdiaagnostic equippment and maake it easier to calculatethee propagation delay of thhe wavefront. This wasshoown by the results in Fig. 9 that the incrrease of the
maaximum numbeer of compounnding did not degrade
d
the
resu
ultant B-modde image in tthe case of plane
p
wave
tran
nsmission. Thhe error in thee calculated propagationpdellay at larger steerings
anglees was consid
dered to besmaller for planne waves thaan for divergiing waves.
Fig
gure 13 showss a longitudinal B-mode im
mage of theheaart of the samme subject as iin Fig. 12 obttained withplaane wave transmission and smaller steering angles.
As can be seen in Fig. 13, a B-mode imag
ge of goodquaality can be obbtained at a veery high framee rate (1010
Hz) that is much higher than thhat (200 Hz) achievedabycon
nventional secctor scanning with a narroow field ofvieew [10].

g. 13. B-mode image of the hheart of the saame subject
Fig
as in Fig. 12 obbtained by parrallel beamforrming withplaane waves andd a smaller mmaximum steeering angle(fraame rate: 10100 Hz).
The
T limitationn of the currennt hardware useduin thepreesent study is thattit takes abbout 1 minutee to prepare
for transmissionn of diverginng waves. DuringD
thispreeparation, an operatoroneeds to fix the possition of theultrrasonic probe without viewiing B-mode im
mages. Thislim
mitation signifiicantly increasses the difficu
ulties of inviv
vo measuremennts, particularrly scanning ofo the same
secction several times. In futture work, we
w need todevvelop a real--time systemm realizing th
he methodpro
oposed in the presentpstudy.

5. ConclusionC
In this studyy, methods for measurrement ofviscoelasticity of arterial walll and evaluattion of red
blo
ood cell aggreggation were ddeveloped. Succh methods
woould be useful forf early diagnnosis of athero
osclerosis.

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