Imaging Parameters on Third Harmonic Transmit Phasing for Tissue Harmonic Generation

Ultrasound in Med. & Biol., Vol. 34, No. 6, pp. 1001–1013, 2008Copyright © 2008 World Federation for Ultrasound in Medicine & Biology

Printed in the USA. All rights reserved0301-5629/08/$–see front matter

doi:10.1016/j.ultrasmedbio.2007.12.001

● Technical Note

IMAGING PARAMETERS ON THIRD HARMONIC TRANSMIT PHASINGFOR TISSUE HARMONIC GENERATION

CHE-CHOU SHEN,* YU-CHUN WANG,* and CHIH-KUANG YEH†

*Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan and†Department of Biomedical Engineering and Environmental Sciences, National Tsing Hua University,

Hsinchu, Taiwan

(Received 21 May 2007, revised 28 November 2007, in final form 3 December 2007)

Abstract—In third harmonic (3f0) transmit phasing, transmit waveforms comprising fundamental (f0) signal and3f0 signal are used to generate both frequency-sum and frequency-difference components for manipulation oftissue harmonic amplitude. Nevertheless, the acoustic propagation of 3f0 transmit signal suffers from more severeattenuation and phase aberration than the f0 signal and hence degrades the performance of 3f0 transmit phasing.Besides, 3f0 transmit parameters such as aperture size and signal bandwidth are also influential in 3f0 transmitphasing. In this study, extensive simulations were performed to investigate the effects of these imaging param-eters. Results indicate that the harmonic enhancement and suppression in 3f0 transmit phasing are compromisedwhen the magnitude of frequency-difference component decreases in the presence of tissue attenuation and phaseaberration. To compensate for the reduced frequency-difference component, a higher 3f0 transmit amplitude canbe used. When the transmit parameters are concerned, a smaller 3f0 transmit aperture can provide more axiallyuniform harmonic enhancement and more effective suppression of harmonic amplitude. In addition, the spectralleakage signal also interferes with tissue harmonics and degrades the efficacy of 3f0 transmit phasing. Our resultssuggest that, in the method of 3f0 transmit phasing, the transmit amplitude, phase and aperture size of 3f0 signalshould remain adjustable for optimization of clinical performance. Besides, multipulse sequences such as pulseinversion are also favorable for leakage removal in 3f0 transmit phasing. (E-mail: [email protected])© 2008 World Federation for Ultrasound in Medicine & Biology.

Key Words: Tissue harmonic signal, 3f0 transmit phasing, Attenuation, Phase aberration, Spectral leakage.

INTRODUCTION

Tissue harmonic signal from finite amplitude distortionof propagating sound wave is generally characterized asprogressive steepening of the waveform as a result of thepressure-dependent acoustic velocity in nonlinear me-dium (Beyer and Letcher 1969; Haran and Cook 1983;Cain 1986). Because the tissue harmonics build up grad-ually with distance from the transducer, the ultrasoundsignal at harmonic frequency is relatively weak in thebeginning of propagation. Consequently, reverberationfrom shallow structures such as interfaces between skinand fat can be markedly suppressed because of the lowecho intensity. Besides, sidelobes of the nonlinearly gen-erated beam are much lower than those of the linearbeam and the corresponding image contrast significantly

Address correspondence to: Che-Chou Shen, Department ofElectrical Engineering, National Taiwan University of Science and
Technology, #43, Sec.4, Keelung Rd., Taipei, 106, Taiwan. E-mail:[email protected]
1001

improves, especially on technically difficult bodies(Christopher 1997, 1998; Tranquart et al. 1999; Desserand Jeffrey 2001).

Even with aforementioned advantages, imagingwith tissue harmonic signal suffers from several difficul-ties. For example, under typical imaging conditions, onlya small amount of harmonic signal is generated duringthe acoustic propagation and thus both penetration andsensitivity of tissue harmonic imaging are limited be-cause of the lower signal-to-noise ratio (Li 1999). On thecontrary, in contrast agent harmonic imaging, wheremicrobubbles are routinely used to enhance image con-trast between blood-perfused areas and tissue back-ground, the presence of tissue harmonics may obstructthe detection of microbubble contrast agents and degradethe contrast-to-tissue ratio (CTR), especially when ahigher mechanical index is adopted (Burns 1996; Changet al. 1996; de Jong and Ten Cate 1996). Because bothenhancement and suppression of tissue harmonic ampli-
tude are essential, respectively, for tissue and contrast
mailto:[email protected]

mailto:[email protected]

1002 Ultrasound in Medicine and Biology Volume 34, Number 6, 2008

imaging, there have been various techniques proposed tomanipulate the tissue harmonic amplitude (Lu andGreenleaf 1991; Krishnan et al. 1998; Christopher 1999;Li and Shen 1999; Zhou and Hossack 2003; Chiao andHao 2005).

We have recently presented a novel method tochange the tissue harmonic amplitude: the third har-monic (3f0) transmit phasing (Shen et al. 2007). Theproposed method is based on transmitting an additional3f0 signal together with the original fundamental signal(f0) to modify the tissue harmonic amplitude. During thenonlinear propagation in tissue, new spectral componentswill be generated at the sum and difference frequenciesof the original transmit signals. These tissue harmonicsignals are referred to as the frequency-sum componentand the frequency-difference component, respectively. Inconventional tissue harmonic imaging, the second har-monic signal is dominated by the frequency-sum com-ponent, which comes from the multiplication of the f0signal with itself. Nevertheless, the frequency-differencecomponent of second harmonic signal can also be pro-duced from the spectral interaction between the f0 signaland the 3f0 signal when the transmit waveform consistsof both signals.

Note that the phase of the frequency-sum compo-nent of second harmonic signal is proportional to 2�f

when the fundamental transmit signal is modeled asexp(j(2�f0t��f)). The symbol �f is the phase of the f0transmit signal. On the other hand, the frequency-differ-ence component is related to both phases of the f0 and 3f0transmit signals. Specifically, the phase of frequency-difference component will be � provided that the 3f0transmit signal is modeled as exp(j(2�(3f0)t��f)).The symbol � represents the relative phase between the3f0 transmit signal and the f0 transmit signal. Conse-quently, tissue harmonic generation can be enhancedwhen the two components are in-phase and being con-structively summed together. Otherwise, they may can-cel out each other and result in reduced tissue harmonicamplitude. In other words, the phase relation between thefrequency-sum and the frequency-difference componentshould be � � 2�f � � for second harmonic suppression,whereas the relation � � 2�f leads to enhancement ofsecond harmonic amplitude. The previously mentionedtwo phase relations suggest that the manipulation ofsecond harmonic amplitude can be achieved by simplytuning the 3f0 transmit phase.

The 3f0 transmit phasing is very different from otherapproaches that simultaneously transmit two frequencies.For example, in differential tissue harmonic imaging(DTHI) from Toshiba, transmission at both f0 and 2f0frequencies is used for additional differential harmonicsignal at f0 frequency (US Patent 2005; Nowicki et al.
2007). Note that there is not spectral overlap between the
differential harmonic signal and the second harmonicsignal and, hence, the resultant harmonic amplitude doesnot rely on the relative phasing between transmit signals.

In 3f0 transmit phasing, generation of frequency-difference component involves the 3f0 transmit signaland thus, both the axial and lateral characteristics of thefrequency-difference component depend on those of theconstitutive 3f0 beam. Compared with the f0 signal, thefocusing of 3f0 signal is typically stronger and the acous-tic power is more concentrated in the axial and lateraldirections. Since the same acoustic power can be deliv-ered to the focal zone with lower transmit amplitude at3f0 frequency due to its stronger focusing, the amplitudeof 3f0 transmit signal can be lower than the f0 transmitamplitude while the generation of frequency-sum andfrequency-difference components are still approximatelyequal in magnitude for maximal cancellation of thesetwo signals. For example, with the same aperture size atboth f0 and 3f0 frequencies, the optimal transmit ampli-tude ratio of the 3f0 signal to the f0 signal is about 0.5 forharmonic suppression (Shen et al. 2007). In other words,for example, the transmit amplitude of the 3f0 signalwould be about 100 kPa for maximal harmonic suppres-sion when the corresponding f0 transmit amplitude is 200kPa.

Nevertheless, because the 3f0 transmit phasing uti-lizes transmission at higher frequency, its performancewould vary with imaging parameters that are sensitive tofrequency. In this technical note, relevant imaging pa-rameters in 3f0 transmit phasing are investigated usingsimulations. This paper is organized as follows. First, theselection of relevant imaging parameters is describedtogether with the simulation model. These imaging pa-rameters are divided into two categories: tissue parame-ters and transmit parameters, and their effects are indi-vidually considered. Finally, conclusions and discussionsof this study will be given.

METHODS

Selection of relevant imaging parametersBecause the 3f0 transmit phasing relies on the fre-

quency-difference component to achieve either construc-tive enhancement or destructive cancellation of the tissueharmonic signal, the beam properties of frequency-dif-ference component would inevitably change the perfor-mance of 3f0 transmit phasing. There are several imagingparameters that could significantly change the frequency-difference component and thus result in degradation of3f0 transmit phasing. For example, the frequency-depen-dent attenuation in biological tissues would markedlyreduce the amplitude of 3f0 signal relative to that of thef0 signal during the acoustic propagation. Consequently,
as compared with the frequency-sum component, the

Imaging parameters for tissue harmonic generation ● C.-C. SHEN et al. 1003

amplitude of frequency-difference component could se-verely decrease such that the efficacy of harmonic en-hancement and suppression is limited. Another frequen-cy-dependent tissue parameter is phase aberration. Withfixed time delay error in transmit/receive channels be-cause of tissue inhomogeneities, the corresponding phaseerror increases with frequency and, hence, results inmore deteriorated beam at higher frequency. Conse-quently, the divergent 3f0 beam may also degrade theperformance of 3f0 transmit phasing.

In addition to those aforementioned tissue parame-ters, transmit parameters such as the aperture size of 3f0transmit signal also play important roles in 3f0 transmitphasing. In enhancement mode, we have shown previ-ously that the depth of focus of the tissue harmonicsignal would become shorter because of the strong fo-cusing of the frequency-difference component (Shen etal. 2007). Consequently, the SNR in harmonic imagingmay deteriorate rapidly for off-focus region. To elongatethe depth of focus in 3f0 transmit phasing, a smaller 3f0transmit aperture can be used to generate a frequency-difference beam with longer depth of focus. The 3f0aperture size can be readily modified in an array systemby changing the number of transmit channels. Besides,when a wideband pulse is transmitted for better axialresolution, the effect of harmonic leakage cannot beignored. The linearly propagated harmonic leakage sig-nal has higher sidelobes than its nonlinear counterpartand thus compromises the image contrast in tissue har-monic imaging (Shen and Li 2001). The leakage signalalso increases the harmonic amplitude in tissue back-ground and hence reduces the specificity of contrastagents in harmonic imaging (Krishnan and O’Donnell1996). Similarly, in 3f0 transmit phasing, the presence ofleakage signal could also deteriorate the efficacy of tis-sue harmonic suppression and cause difficulties in thedetection of contrast harmonic signal.

Based on these observations, relevant imaging pa-rameters including attenuation, phase aberration, 3f0transmit aperture size and transmit signal bandwidth areconsidered for their effects on 3f0 transmit phasing in thisstudy.

Simulation modelIn the simulation model, the transmit waveform is

first decomposed into discrete temporal frequency com-ponents. For each frequency component, continuousbeam formation is approximated by incremental fieldpropagation. At each increment, linear propagation issimulated based on the angular spectrum method (Good-man 1968; Liu and Waag 1997). The nonlinear propa-gation is modeled using the finite amplitude distortion
model (Christopher 1997). As shown in the following
equation, the finite amplitude distortion model utilizesthe frequency domain solution to Burgers’ equation, i.e.

un � u�n � j

��f�z

2c2 ��k�1

n�1

ku�ku

�n�k � �

k�n

N

nu�ku

�k�n*� (1)

In eqn (1), �z is the propagation increment alongthe axial direction. The fundamental frequency is de-noted by f and � is a parameter representing the nonlin-earity of the propagation medium. The term un

� denotesthe temporal velocity field at frequency nf (n is aninteger) after linear propagation. Likewise, un denotesthe temporal velocity field after nonlinear propagation.The sound velocity is denoted by c. A one-dimensional,64-channel linear array is assumed to transmit the2-MHz fundamental signal together with the correspond-ing 3f0 signal at 6 MHz. The array had a 0.3-mm pitchand the transmit focus was set to 55 mm away from thetransducer. The propagation medium was assumed to behomogeneous unless particularly specified and the non-linear parameter � was set to 3.5, approximating thenonlinear property of water (Law et al. 1985). For sim-plicity, frequency response of the transducer is ignoredwithout loss of generality. In the simulation model, trans-mit signals of either continuous wave (CW) or pulsewave (PW) can be adopted. For a CW case, the harmonicsignals are represented as the corresponding Fourier se-ries of the transmit waveform. For a PW case, the sim-ulated second harmonic signal is extracted by band-passfiltering, with a flat frequency response between 3 MHzand 5 MHz. For both CW and PW transmit, the peakacoustic pressure at fundamental frequency is 200 KPa.For the 3f0 transmit signal, its acoustic pressure is deter-mined by the 3f0 amplitude ratio and its phase can bechanged from –170° to 180°.

RESULTS

Effects of tissue parameters

Attenuation. CW simulations were performed tostudy the effect of frequency-dependent attenuation on3f0 transmit phasing. Attenuation coefficients of 0.02,0.06 and 0.11 np/cm/MHz were considered, which cor-respond to the attenuation in blood, fat and liver tissues,respectively (Shung et al. 1992). The simulated secondharmonic axial amplitudes, lateral beam patterns and thecorresponding integrations of beam pattern are demon-strated with � 0.06 np/cm/MHz in Fig. 1d–f, respec-tively. For comparison, corresponding results withoutattenuation (i.e., � 0 np/cm/MHz) are also illustratedin Fig. 1a–c, respectively. In these simulations, the am-plitude ratio of 3f0 transmit signal is fixed at 0.5. In Fig.
1a and d, the axial amplitudes of both enhancement mode

. Right


and suppression mode are normalized to the focal am-plitude without 3f0 transmit for each value. In otherwords, the normalized amplitude will be larger than unityif the 3f0 transmit signal results in enhancement of har-monic amplitude. Otherwise, the suppression of har-monic generation will make the normalized amplitudeless than unity.

Figure 1d shows that, after attenuation, the 3f0 trans-mit phasing is still effective for both enhancement andsuppression of second harmonic signal over a wide rangeof axial depths. However, it should be noted that theperformance of 3f0 transmit phasing is degraded com-pared with that without attenuation. Specifically, thefocal enhancement is reduced from about 6 dB withoutattenuation to only 3 dB with � 0.06 np/cm/MHz. Thecorresponding focal suppression is also reduced fromabout 11 dB without attenuation to only 6 dB with �0.06 np/cm/MHz. In other words, when tissue attenua-tion is considered, 3f0 transmit phasing results in lesschange of second harmonic amplitude.

Similar observations can be made from the beampatterns. In Fig. 1b and e, the focal beam patterns arenormalized to the on-axis amplitude without 3f0 transmitfor each value. Specifically, without tissue attenuation,the beam pattern of enhancement mode is more concen-trated (i.e., lower sidelobes and narrower mainlobe) suchthat the corresponding lateral and contrast resolution aresuperior to that without 3f0 transmit. Nevertheless, aftertissue attenuation, the radiation patterns of both enhance-ment and suppression modes become more similar to that

Fig. 1. Simulated second harmonic axial amplitudes, beamLeft: � 0 np/cm/MHz

without 3f0 transmit. Although the enhancement beam

still has lower sidelobes, the improvement of imagequality has been compromised because of attenuation.The integrated beam patterns in Fig. 1c and f also revealthat the profiles tend to be more close to each other whenthe attenuation is present.

The variation of second harmonic amplitude with3f0 transmit phase at focal depth is also shown in Fig. 2.For each value, the focal second harmonic amplitudesare normalized to that without 3f0 transmit signal. It isclearly demonstrated that the extent of enhancement andsuppression using 3f0 transmit phasing decreases with theattenuation. The results are as expected because a smalleramount of frequency-difference component would begenerated at second harmonic frequency when its con-stitutive 3f0 transmit beam suffers from severe attenua-tion during propagation. However, it is also noticeable inFig. 2 that the 3f0 transmit phases for maximal enhance-ment and suppression are insensitive to tissue attenua-tion. For example, the 3f0 transmit phase for maximalsuppression only slightly drifts from –60° to –40° whenthe increases from 0 np/cm/MHz to 0.11 np/cm/MHz.

Because the magnitude of 3f0 transmit beam ismarkedly reduced in the presence of attenuation and thusproduces insufficient frequency-difference component,the 3f0 transmit amplitude at source should be increasedto compensate the attenuated frequency-difference com-ponent. Figure 3 shows the focal second harmonic am-plitudes as a function of 3f0 transmit amplitude ratio withdifferent attenuations. It is demonstrated that the 3f0transmit amplitude ratio for optimal suppression obvi-

rns and integrated beam patterns with different values.: � 0.06 np/cm/MHz.

patte

ously increases with attenuation. For example, the 3f0

de ratio


amplitude ratio should increase to 0.55, 0.9 and 1.5,respectively, with � 0.02, 0.06 and 0.11 np/cm/MHz.In other words, when the tissue attenuation cannot beignored, a higher 3f0 transmit amplitude is required tocompensate the signal loss of frequency-difference com-ponent for better harmonic suppression. In addition, itshould be noted that the harmonic enhancement wouldalso benefit from the stronger 3f0 transmit signal.

Fig. 2. Simulated focal second harmonic amplitudes as atransmit amplitu

Fig. 3. Simulated focal second harmonic amplitudes as a
3f0 transmit phase is fixed a
Phase aberrationIn this study, PW simulations were performed to

investigate the effect of phase aberration on 3f0 transmitphasing. In the simulations, a displaced phase screen wasincluded to model sound velocity variations between twodifferent media. Such a model is similar to the oneproposed in Liu and Waag (1994). The medium next tothe transducer had a propagation velocity of 1.45 mm/s,

on of 3f0 transmit phase with different values. The 3f0is fixed at 0.5.

n of 3f transmit amplitude with different values. The

functi

functio
0
t suppression mode.


a uniform thickness of 15 mm and a � of 6 to mimic thenonlinear properties of fat tissue (Law et al. 1985). Thedeeper medium is assumed to be water with a thicknessof 65 mm. Time delay errors resulting from irregularthickness of fat tissue were simulated using a 2-D phasescreen at the boundary of the two media. The phasescreen had a correlation length of 5 mm and can bescaled to include different extent of phase error. Forconvenience, the phase screens with root-mean-square(RMS) time delay error of 11.6, 23.3 and 46.6 ns arereferred to as 1� aberration, 2� aberration and 4�aberration, respectively, in this paper. Gray level imageof the 4� aberration pattern is shown in Fig. 4.

Figure 5a and c show the beam patterns at focaldepth without aberration and with 4� aberration, respec-

Fig. 4. Pattern of time delay error for 4� aberration. Positivephase shift is displayed in white and the negative shift is in

black.

Fig. 5. Simulated second harmonic beam patterns and in
(right).
tively. Note that the corresponding 46.6-ns RMS timedelay error with the 4� aberration is relatively largecompared with those measured in biological tissue(Hinkelman et al. 1994, 1995) and thus significant beamdistortion is expected. Compared with the case in homo-geneous tissue, the beam patterns with phase aberrationare markedly distorted and the resultant sidelobe levelsare elevated for both enhancement and suppression. Sim-ilar observations can be made using the integrated beampatterns in Fig. 5b and d. The profile of enhancementmode converges to unity much slower compared with itsno-aberration counterpart. It is also shown that, unlikethe distinct difference among integration profiles withoutaberration, the profile of harmonic enhancement be-comes similar to that without 3f0 transmit when theaberration is present. In other words, the beam quality ofsecond harmonic signal in 3f0 transmit phasing is signif-icantly degraded by phase aberration.

The variation of focal second harmonic amplitudeas a function of 3f0 transmit phase is also demonstratedusing simulations in Fig. 6 with different aberrations. Foreach aberration, the second harmonic amplitudes with 3f0transmit are normalized to that without 3f0 transmit.Figure 6 shows that both enhancement and suppressionof second harmonic amplitude tend to be compromisedwhen the phase error increases. It is also shown, how-ever, that the presence of phase aberration does not resultin significant change of 3f0 transmit phase for eitherharmonic enhancement or suppression. For example, themaximal harmonic suppression without aberration is

ed beam patterns without (left) and with 4� aberration
tegrat

ude ra


achieved with a 3f0 transmit phase of 120°. When the 4�aberration is included, the 3f0 transmit phase for maximalharmonic suppression slightly drifts to 140°. In otherwords, although the presence of phase aberration reducesthe efficacy of both harmonic enhancement and suppres-sion, the corresponding 3f0 transmit phase remains rela-tively unchanged.

Effects of transmit parameters3f0 transmit aperture size. In this study, the relative

size of 3f0 aperture to the fundamental aperture is con-sidered using CW simulations. In Fig. 7, the focal secondharmonic amplitudes are represented as a function ofboth amplitude ratios and phases of 3f0 transmit signal.The 3f0 aperture sizes are 100%, 75% and 50% of thefundamental aperture size, respectively, in Fig. 7a–c.Note that, for example, the 50% 3f0 aperture uses thecentral 32 channels for transmit, whereas the fundamen-tal aperture comprises the whole 64 channels. The focalsecond harmonic amplitudes in Fig. 7 have been normal-ized to that without 3f0 transmit for each 3f0 aperture andthe gray bar in each panel maps the normalized harmonicamplitudes into gray levels.

In Fig. 7a, it is apparent that the most effectivesuppression of second harmonic signal with the 100% 3f0aperture is achieved when the 3f0 transmit amplituderatio is scaled to about 0.45. Nevertheless, it is shown inFig. 7b and c that the maximal harmonic suppressionoccurs with a higher 3f0 transmit amplitude when asmaller 3f0 aperture is used. For example, the optimal

Fig. 6. Simulated focal second harmonic amplitudes as a3f0 transmit amplit

ratios for harmonic suppression change to 0.55 and 0.8,

respectively, for the 75% and 50% 3f0 apertures. Theincrease of 3f0 transmit amplitude ratio is as expectedbecause a higher amplitude is necessary to maintainsimilar 3f0 transmit energy with a reduced aperture size.For all figures, it is also obvious that the harmonicenhancement monotonically increases with the 3f0 trans-mit amplitude. Moreover, the 3f0 transmit phases corre-sponding to harmonic enhancement and suppression donot change with different aperture sizes. For example,the 3f0 transmit phase for harmonic suppression remainsat –60° when the 3f0 aperture decreases from 100% to50%.

The second harmonic axial amplitudes and the lat-eral beam patterns in enhancement mode are shown inFig. 8a and b for different 3f0 apertures. Note that, inboth Fig. 8 and Fig. 9, different 3f0 transmit amplitudesare selected for different apertures based on the results inFig. 7 to achieve maximal suppression of harmonic am-plitude. When the 3f0 aperture size is reduced from 100%to 75% and 50%, the corresponding second harmonicamplitudes become more uniformly distributed in theaxial direction and thus provide longer depths of focus.Nevertheless, it should be noted that the long depth offocus is achieved at the cost of image quality. As shownin Fig. 8b, for a smaller 3f0 aperture, the mainlobebecomes wider and the sidelobe levels are also elevated.Consequently, the image resolution and image contrastcan be compromised because of the less directive beam.

In suppression mode, the 3f0 transmit aperture alsoplay an important role to optimize the harmonic suppres-

ion of 3f0 transmit phase with different aberrations. Thetio is fixed at 0.5.

funct

sion in both axial and lateral directions. As shown in Fig.

m left


9a, although similar harmonic suppression at focal depthcan be achieved with different sizes of 3f0 apertures, theprefocal and postfocal second harmonic amplitudes be-come elevated with a reduced 3f0 aperture size. In theextreme case of 50% 3f0 aperture, the harmonic suppres-sion is effective only at focal depth. Nevertheless, it isnoticeable that the 75% 3f0 aperture not only provideseffective harmonic suppression for a wide range of axialdepths, the corresponding radiation pattern in Fig. 9balso has the lowest magnitude in the mainlobe regioncompared with the other two apertures. In other words,harmonic suppression with the 75% 3f0 aperture is ef-fective over a larger range in both axial and lateraldirections such that the tissue background in contrastimaging can be better suppressed.

Transmit bandwidthIn 3f0 transmit phasing, the presence of leakage

harmonic signal would interfere with the frequency-sumand the frequency-difference components of tissue har-monic signal. PW simulations were performed to illus-trate two different conditions of spectral leakage in 3f0transmit phasing. Condition I occurs when the transmitsignals at both f0 and 3f0 frequencies are wideband pulsessuch that the leakage signals come from both the funda-mental transmit band and the 3f0 transmit band. Specif-ically, the transmit signal is a Gaussian pulse with a –6

Fig. 7. Simulated focal second harmonic amplitudes as awith different 3f0 transmit aperture sizes. Fro

dB bandwidth of about 1.6 MHz at both f0 and 3f0

frequencies, which contains considerable spectral energyat second harmonic band. In Condition II, however, thebandwidth of the 3f0 transmit signal is reduced to about0.6 MHz to avoid spectral leakage from the 3f0 transmitband. In other words, the f0 transmit pulse is widebandand the 3f0 transmit pulse is narrowband in Condition II.

For Condition I shown in Fig. 10a–c, although theharmonic suppression mode still provides lower axial am-plitudes than the enhancement mode, it should be noted thatthe second harmonic amplitudes are already higher thanthose without 3f0 transmit for all depths because of theadditional leakage signal from the 3f0 transmit band. Con-sequently, the 3f0 transmit phasing does not provide anytissue suppression compared with the case without 3f0transmit and, hence, no CTR improvement is expected incontrast harmonic imaging. For harmonic enhancement, theincrease of harmonic amplitude is also reduced from 6 dBto about 3 dB in the presence of spectral leakage. It is alsoshown that the sidelobes of all beam patterns are markedlyelevated because of the leakage signal such that all integra-tion profiles converge slowly and become less distinguish-able as compared with Fig. 5b, where no spectral leakage isconsidered.

For Condition II, however, only spectral leakage fromthe fundamental band is present because the narrowband 3f0transmit pulse produces negligible leakage signal. Asshown in Fig. 10d, the second harmonic amplitude at source

on of 3f0 transmit phase and 3f0 transmit amplitude ratioto right: 100%, 75% and 50%, respectively.

functi

in both enhancement and suppression mode is equal to that

monic


without 3f0 transmit. Accordingly, the tissue harmonic am-plitude can be better suppressed as the sound wave propa-gates. Furthermore, when the harmonic enhancement isconsidered, the beam quality of tissue harmonic signal isapparently superior to that without 3f0 transmit and, hence,the corresponding integration profile in Fig. 10f rises morerapidly than others. Nevertheless, although the 3f0 transmitphasing performs better in Condition II, it should be notedthat the sidelobes in enhancement beam is still much highercompared with those without leakage (i.e., in Fig. 5a) andthus the loss of contrast resolution in tissue harmonic im-

Fig. 8. (a) Simulated second harmonic axial amplitudes wis fixed at enhancement mode. (b) Simulated second har

aging is inevitable. In addition, the presence of leakage

signal increases harmonic amplitudes, especially in the nearfield and, hence, the efficacy of harmonic suppression in 3f0transmit phasing is still limited in Condition II.

DISCUSSION

Although this study is performed without presentingreal ultrasound images, information about possible vari-ation of image quality in 3f0 transmit phasing has beenprovided without loss of generality by comparing thesimulated acoustic beams. In the simulations, it is as-

ferent 3f0 transmit aperture sizes. The 3f0 transmit phasebeam patterns with different 3f0 transmit aperture sizes.

ith dif

sumed that the dispersion effect characterized as varia-

onic b


tion of sound velocity with frequency is negligible. Nev-ertheless, the dispersion could lead to different distortionof the f0 and 3f0 beams and further degrade the method of3f0 transmit phasing. Therefore, adequate time delaycorrection can be applied at the transmit part of theimaging system so as to avoid severe distortion of 3f0transmit beam and the corresponding frequency-differ-ence signal. Results also indicate that tissue characteris-tics such as frequency-dependent attenuation and tissueinhomogeneities can result in significant decrease of themagnitude of 3f0 signal during propagation. Conse-

Fig. 9. (a) Simulated second harmonic axial amplitudes wis fixed at suppression mode. (b) Simulated second harm

quently, the achievable harmonic enhancement and sup-

pression are also reduced because of the lower frequen-cy-difference magnitude in the presence of tissue atten-uation and phase aberration. To compensate for themagnitude loss of 3f0 signal during propagation, a highertransmit amplitude at 3f0 frequency can be used to gen-erate sufficient frequency-difference component so as tocancel with the frequency-sum component for maximalharmonic suppression. The higher transmit amplitude at3f0 frequency is also necessary in the case of a smaller3f0 aperture.

Because the 3f0 transmit phasing is sensitive to

ferent 3f0 transmit aperture sizes. The 3f0 transmit phaseeam patterns with different 3f0 transmit aperture sizes.

ith dif

the parameters of propagation tissue, which cannot be

eft: C


known in advance, the optimal phase and amplitude of3f0 transmit signal could vary significantly in differentclinical applications. Consequently, imaging calibra-tion is required to select these 3f0 transmit parameters.This kind of calibration can be performed automati-cally by measuring the tissue harmonic amplitudeswith different combinations of 3f0 transmit amplitudeand phase. For example, the 3f0 transmit amplitudeand phase that result in the lowest tissue harmonicamplitude should be used for harmonic suppression inthat particular condition. Moreover, it should be notedthat the 3f0 transmit phase that corresponds to theenhancement or suppression of tissue harmonic signalis quite invariant to tissue parameters. This phenom-enon can help to facilitate the search of optimal 3f0

transmit phases in the calibration.Our results also show that there is a trade-off

between image contrast and image resolution in 3f0

transmit phasing because the wide transmit bandwidthat either f0 or 3f0 frequencies markedly degrades theharmonic enhancement and suppression. Nevertheless,the limitation can be avoided when the multipulsetransmit scheme such as pulse inversion (PI) isadopted to remove the leakage signal (Simpson et al.1999; Shen and Li 2002). The PI technique involvestwo firings with inverted waveforms for each acousticbeam line. When the returning echoes from the twofirings are summed, the linearly propagated leakagesignal is cancelled and only nonlinearly generated

Fig. 10. Simulated second harmonic axial amplitudes,conditions of spectral leakage. L

tissue harmonic signal remains. For example, with the

same wideband transmit pulse as in Condition I of Fig.10, the beam patterns in Fig. 11 clearly reveal that thePI technique can restore the contrast resolution intissue harmonic imaging by providing much lowersidelobes than those without PI technique.

CONCLUSIONS

In this paper, the performance of 3f0 transmit phas-ing on tissue harmonic generation is studied with variousimaging parameters. It is demonstrated that the 3f0 trans-mit signal is susceptible to tissue parameters such astissue attenuation and beam distortion during acousticpropagation. Consequently, in clinical applications of 3f0transmit phasing, imaging calibration is suggested todetermine the optimal phase and amplitude of the 3f0transmit signal.

It is also shown that the transmit parameters such asaperture size and bandwidth significantly change thetissue harmonic generation in 3f0 transmit phasing. Com-pared with using the same aperture size for both f0 and3f0 transmit, a smaller 3f0 aperture can provide moreeffective harmonic suppression over a larger region inboth axial and lateral directions for contrast harmonicimaging. With imaging parameters used in this study, theoptimal 3f0 transmit aperture for harmonic suppression isabout 75% of the f0 aperture size. When harmonic en-hancement is concerned in tissue harmonic imaging, a

patterns and integrated beam patterns with differentondition I. Right: Condition II.

beam

smaller 3f0 aperture is also favorable when more uniform

cemen


harmonic amplitudes in the axial direction are preferredfor longer depth of focus.

The selection of transmit bandwidth at both f0 and3f0 frequencies also markedly change the efficacy of 3f0transmit phasing on harmonic enhancement and suppres-sion. When the wideband transmit pulses are used forbetter axial resolution, the spectral leakage signal de-grades the beam quality in tissue harmonic imaging withdecreased harmonic enhancement. On the other hand, theleakage signal also reduces the achievable suppression oftissue background in contrast harmonic imaging. There-fore, removal of spectral leakage signal using multipulsetransmit scheme such as PI technique is beneficial in 3f0transmit phasing.

Acknowledgments—Supported in part by the National Science Councilof Taiwan under grant NSC 96-2221-E-011-143 and Intelligent Build-ing Research Center of National Taiwan University of Science andTechnology are gratefully acknowledged. We also thank the reviewersfor the helpful comments.

REFERENCES

Beyer RT, Letcher SV. Nonlinear Acoustics. New York: Academic,1969.

Burns PN. Harmonic imaging with ultrasound contrast agents. ClinRadiol 1996;51(Suppl 1):50–55.

Cain CA. Ultrasonic reflection mode imaging of the nonlinear param-eter B/A. I: A theoretical basis. J Acoust Soc Am 1986;80:28–32.

Chang PH, Shung KK, Levene HB. Quantitative measurements ofsecond harmonic Doppler using ultrasound contrast agents. Ultra-sound Med Biol 1996;22:1205–1214.

Christopher T. Finite amplitude distortion-based inhomogeneous pulse

Fig. 11. Simulated second harmonic beam patterns withat enhan

echo ultrasonic imaging. IEEE Trans Ultrason Ferroelectr FreqControl 1997;44:125–139.

Christopher T. Experimental investigation of finite amplitude dis-tortion-based second harmonic pulse echo ultrasonic imaging.IEEE Trans Ultrason Ferroelectr Freq Control 1998;45:158 –162.

Christopher T. Source prebiasing for improved second harmonic bub-ble-response imaging. IEEE Trans Ultrason Ferroelectr Freq Con-trol 1999;46:556–563.

Chiao RY, Hao X. Coded excitation for diagnostic ultrasound: a systemdeveloper’s perspective. IEEE Trans Ultrason Ferroelectr FreqControl 2005;52:160–170.

de Jong N, Ten Cate FJ. New ultrasound contrast agents and techno-logical innovations. Ultrasonics 1996;34:587–590.

Desser TS, Jeffrey RB. Tissue harmonic imaging techniques: Physicalprinciples and clinical applications. Semin Ultrasound CT MR2001;22:1–10.

Goodman JW. Introduction to Fourier Optics. New York: McGraw-Hill, 1968.

Haran ME, Cook BD. Distortion of finite amplitude ultrasound in lossymedia. J Acoust Soc Am 1983;73:774–779.

Hinkelman LM, Liu DL, Metlay LA, Waag RC. Measurements ofultrasonic pulse arrival time and energy level variations producedby propagation through abdominal wall. J Acoust Soc Am 1994;95:530–541.

Hinkelman LM, Liu DL, Waag RC, Zhu Q, Steinberg BD. Measure-ment and correction of ultrasonic pulse distortion produced by thehuman breast. J Acoust Soc Am 1995;97:1958–1969.

Krishnan S, Hamilton JD, O’Donnell M. Suppression of propagatingsecond harmonic in ultrasound contrast imaging. IEEE Trans Ul-trason Ferroelectr Freq Control 1998;45:704–711.

Krishnan S, O’Donnell M. Transmit aperture processing for nonlinearcontrast agent imaging. Ultrason Imaging 1996;18:77–105.

Law WK, Frizzell LA, Dunn F. Determination of the nonlinearityparameter B/A of biological media. Ultrasound Med Biol 1985;11:307–318.

Li PC. Pulse compression for finite amplitude distortion based har-monic imaging using coded waveforms. Ultrason Imaging 1999;21:1–16.

Li PC, Shen CC. Effects of transmit focusing on finite amplitudedistortion based second harmonic generation. Ultrason Imaging

d with the PI technique. The 3f0 transmit phase is fixedt mode.

out an

1999;21:243–258.


Liu DL, Waag RC. Correction of ultrasonic wavefront distortion usingbackpropagation and a reference waveform method for time-shiftcompensation. J Acoust Soc Am 1994;96:649–660.

Liu DL, Waag RC. Propagation and backpropagation for ultrasonicwavefront design. IEEE Trans Ultrason Ferroelectr Freq Control1997;44:1–12.

Lu JY, Greenleaf JF. Pulse-echo imaging using a nondiffracting beamtransducer. Ultrasound Med Biol 1991;17:265–281.

Nowicki A, Wójcik J, Secomski W. Harmonic imaging using multitonenonlinear coding. Ultrasound Med Biol 2007;33:1112–1122.

Shen CC, Li PC. Harmonic leakage and image quality degradation intissue harmonic imaging. IEEE Trans Ultrason Ferroelectr FreqControl 2001;48:728–736.

Shen CC, Li PC. Motion artifacts of pulse inversion-based tissueharmonic imaging. IEEE Trans Ultrason Ferroelectr Freq Control
2002;49:1203–1211.
Shen CC, Wang YC, Hsieh YC. Third harmonic transmit phasing fortissue harmonic generation. IEEE Trans Ultrason Ferroelectr FreqControl 2007;54:1370–1381.

Shung KK, Smith MB, Tsui B. Principles of Medical Imaging. NewYork: Academic, 1992.

Simpson DH, Chin CT, Burns PN. Pulse inversion doppler: a newmethod for detecting nonlinear echoes from microbubble contrastagents. IEEE Trans Ultrason Ferroelectr Freq Control 1999;46:372–382.

Tranquart F, Grenier N, Eder V, Pourcelot L. Clinical use of ultrasoundtissue harmonic imaging. Ultrasound Med Biol 1999;25:889–894.

US Patent 6899679. Ultrasonic diagnosis apparatus and ultrasoundimaging method; 2005.

Zhou S, Hossack JA. Dynamic-transmit focusing using time-dependentfocal zone and center frequency. IEEE Trans Ultrason Ferroelectr
Freq Control 2003;50:142–152.

Documents

Imaging Parameters on Third Harmonic Transmit Phasing for Tissue Harmonic Generation