ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 55, no. 1, january 2008 249

Correspondence

Improved Contrast Ultrasound with TissueHarmonic Minimizing Pulse

Kajoli B. Krishnanand Kai E. Thomenius, Member, IEEE

Abstract—We have computed predistorted pulses thatminimize tissue harmonics to � �25 dB compared to fun-damental over a 4-cm depth in the focal region using a Han-kel transform-based algorithm. The results indicate theirpotential in achieving patient independent improvementin contrast with microbubbles using wideband ultrasonictransducers at high mechanical indices.

I. Introduction

Contrast agents such as gas bubbles exhibit nonlinearoscillations in the presence of insonifying frequency. In

ultrasonic imaging with contrast agents, the goal is to de-tect the location of the bubbles by tracking their harmonicechoes to enhance the contrast between blood and sur-rounding tissue. However, harmonics generated during thepropagation of ultrasound through tissue at high mechan-ical indices (MI) can confound the detection process [1],[2]. Bubbles for improved contrast resolution in B-modeimages in ultrasound and developments in the widebandtransducer technology have led to a spurt in harmonicimaging in recent years. Thus, there is a definite needto minimize the effects of nonlinear propagation, nonlin-ear pulsers, and transduction such as capacitive microma-chined ultrasound transducers (cMUT).

Over the last decade, several researchers have suggestedthe use of prebiased transmit pulses to improve the detec-tion of contrast harmonics [2]–[6]. Hossack et al. [3] pro-posed a method for shaping the envelope of the transmitwaveform to nullify the effect of nonlinearities of the trans-ducer and achieve a line focus. Krishnan et al. [2] devel-oped a harmonic cancellation system by backpropagatingthe second harmonic from the ultrasonic field to the trans-ducer array; and they used the resultant signal to predis-tort the transmit pulse to reduce harmonic generation dueto tissue propagation. Their approach did not account forfrequency-dependent attenuation and was based on a non-linear propagation of the transmit waveform and a linearbackpropagation of the second harmonic. Christopher [4]used a Hankel-transform approach to model diffraction,

Manuscript received March 27, 2007; accepted August 26, 2007.K. B. Krishnan is with GE Global Research, GE India Tech-

nology Centre, Bangalore 560066, India (e-mail: kajoli.krishnan@geind.ge.com).

K. E. Thomenius is with GE Global Research, Niskayuna, NY12309.

Digital Object Identifier 10.1109/TUFFC.2008.634

dispersion, attenuation, and nonlinear propagation of ul-trasound to prebias a single transmit frequency with a sec-ond harmonic content created by linearly backpropagatingthe second harmonic from the focal plane to the trans-ducer face. Hossack [5] and Fraser [6] devised methods toprebias the transmit waveform to counter the second har-monics generated due to the nonlinear response of cMUTthat are otherwise characterized by highly desirable, widebandwidth and enhanced sensitivity to low-level acousticsignals. More recently, Lazenby [7] proposed a generalizedscheme of delays and sign changes in the transmit wave-form to enable transmit harmonic suppression from com-plex waveform generators that include the harmonic can-cellation system of Krishnan et al. [2].

We have, like Christopher [4], used a Hankel-transformapproach [8]–[10] to generate the modified, predistortedharmonic minimizing (HARM) pulse. However, we used anovel minimization method, in which, unlike Christopher,we first propagate the undistorted pulse linearly to focuswith no harmonics, then backpropagate the resulting fo-cal pulse nonlinearly to the transducer face to generatea predistorted HARM pulse. The method of generatingHARM pulses and the simulation parameters is summa-rized in Section II. The results of HARM pulse propaga-tion in liver, methods to improve MI, and the applicationof HARM pulses to layered medium are presented in Sec-tion III. Implications for patient-independent imaging arediscussed in Section IV.

II. Methods

We compute the HARM pulses by linearly propagat-ing the undistorted pulse to focus, then backpropagat-ing the focal pulse nonlinearly to the transducer face,thereby coding it with tissue characteristics. When the re-sulting pulse is forward-propagated nonlinearly to focus,the tissue-generated harmonics are minimized in the focalregion in a process of phase cancellation. Our implementa-tion of the pulse propagation algorithm is based on the an-gular spectrum approach used by Christopher and Parker[8], [9], and Christopher [10].

We performed simulations with an overall fractionalbandwidth of 100% centered at 3 MHz. The transmit sys-tem is centered at 2 MHz with a bandwidth of 50%, andthe second harmonic signal is received at 4 MHz. Theseare typical frequencies used in harmonic imaging of the ab-domen and the heart and assume minimal second harmonicat transmit. The overall bandwidth restricts the amount ofharmonic that can be present in the predistorted pulse to4.5 MHz. A circular aperture of 25-mm diameter is usedfor the simulations. The spectral distribution and wave-form of the transmit pulse and the aperture apodization is

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250 ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 55, no. 1, january 2008

Fig. 1. A 2 MHz centered Gaussian pulse of a 25-mm diameter,50% bandwidth transducer. (a) Spectral distribution. (b) Waveform.(c) Aperture apodization.

shown in Fig. 1. A finite value of taper is used to keep outthe propagation-process-related noise. The axial step sizefor the simulations is 0.5 mm. A typical abdominal depthup to 16 cm is considered. Simulations are performed forf-numbers 1 to 5.

HARM pulses are generated for liver-like tissue with afrequency-dependent attenuation coefficient of 0.03 and apower law index of 1.3 that is typical of tissue-like medium[8]–[11]. The nonlinearity parameter, a measure of the de-parture of the propagation process from the linear char-acter of ordinary acoustics due to finite amplitude of thesound beam in tissue, is set at 4.7 [8]–[10], [12]. We havearbitrarily defined the goal of minimization to achieve asecond harmonic level of < −25 dB over a depth of atleast 4 cm along the propagation path with respect tothe fundamental. For typical transmit amplitudes, the ra-tio of the second harmonic amplitude to the fundamentalamplitude for a typical contrast agent has been reportedas −10 dB [13]. HARM pulses are designed to have tis-sue harmonics few orders of magnitude below the contrastharmonic over a typical depth for clinical application. Thestudy is focused on generating medium to high MI pulses(∼MI > 0.8) as there is little second harmonic producedat lower acoustic intensities.

III. Results

A. Characteristics of HARM Pulses

The spectral distribution of HARM pulses in liver com-puted using the forward and the backpropagation algo-rithm shown in Fig. 2 for f-numbers 2–5 illustrates the in-crease in harmonic content with an increase in focal depth.

The harmonic component in the HARM pulse needsto be understood in the context of forward propagationof the 2 MHz Gaussian pulse at the MIs correspondingto each focal number. At every step, the backpropagationalgorithm adds the energy that would have been atten-uated to produce the normal focal spectral distributionin the forward propagation process. The harmonic energycontent in the HARM pulse is so high because the abso-lute energy content of the second harmonic that has to beminimized at the focus is high. In addition to that, theaccumulative effect of the nonlinearity parameter resultsin the backpropagation algorithm to add energy nonlin-early to the HARM with an increase in focal depth. As

Fig. 2. Spectral distribution of HARM pulses in liver. (a) f-number 2,MI = 1. (b) f-number 3 MI = 0.7. (c) f-number 4 MI = 0.35. Note thegeneral increase in the harmonic content of HARM pulse generatedfrom large focal depths.

Fig. 3. A 25-mm diameter transducer focused at 10 cm, f-number 4,MI = 0.35 in liver. (a) Axial beam profiles of the second harmonicof 2 MHz Gaussian (––) and clipped 2 MHz HARM (----) pulse nor-malized with respect to the fundamental. The very steep drop of thesecond harmonic energy with the HARM pulse is clearly evident atthe design depth of 100 mm. (b) Waveform of clipped 2 MHz HARMpulse. The clipped HARM pulse minimizes the second harmonic to< −25 dB with respect to the fundamental over a > 4 cm depth.

a consequence, HARM pulses can become “shocked” andpresent a limiting utility for the algorithm at high MIs forlong focal depths. Christopher [4] had also encountered asimilar limitation with his harmonic minimizing approach.

The axial propagation of the second harmonic of 2 MHzGaussian pulse and clipped 2 MHz HARM pulse for f-number 4, normalized with respect to the fundamentalis shown in Fig. 3(a). We define a clipped HARM pulseas one that has the necessary spectral content to achieveour goal of harmonic minimization. Fig. 3(b) presents thewaveform of clipped HARM pulse with spectral contentup to 4.5 MHz for the successful reduction of harmonicenergy with the HARM pulse near the depth of 100 mmas shown in Fig. 3(a). Due to the relatively low MI = 0.35,the tissue harmonics generated by the unmodified, con-ventional pulse barely exceed −25 dB with respect to thefundamental frequency. The nonlinear growth of the spec-tral content of the HARM pulse indicates a need to devisealternate mechanisms for generating high MI pulses forimaging longer depths of tissue.

B. High MI HARM Pulses

We propose two mechanisms to overcome the limita-tions of the algorithm to design high MI HARM pulses forminimizing harmonics at greater focal depths.

krishnan and thomenius: contrast ultrasound with harmonic minimizing pulse 251

Fig. 4. A 25-mm diameter transducer focused at 10 cm depth. Axialpropagation of the second harmonic of high amplitude 2 MHz Gaus-sian (––) and clipped HARM (----) pulse normalized with respect tothe fundamental in liver at f-number 4. (a) Twice the amplitude atMI = 0.7. (b) Three times the amplitude at MI = 1.0. Note thatharmonics of the HARM pulse are < −25 dB with respect to thefundamental over a > 4 cm depth in (a) and not in (b).

First, high MI can be achieved by using higher am-plitude HARM pulses that are computed from transmitpulses of lower MIs. For a transmit pulse of amplitudeA, the on-axis second harmonic content is proportional toA2. The second harmonic cancellation achieved by the cor-responding clipped HARM pulse is ∼A2. Likewise, for atransmit pulse of amplitude 2A, the on-axis second har-monic content is proportional to 4A2. However, the highMI HARM pulse designed by the proposed method couldbe expected to demonstrate limited second harmonic can-cellation ∼2A2. This leads to a residual second harmonic ∼(4A2-2A2) = 2A2 and a factor of 2 between the second har-monic of high MI undistorted pulse and high MI HARMpulse. In Fig. 4(a) and (b), we depict the axial propagationof two and three times the amplitude of the clipped HARMpulse shown in Fig. 3(b) with the corresponding nonlinearpropagation of two and three times the amplitude of the2 MHz Gaussian in liver at a MI = 0.7 and 1.0 respectively.As anticipated, HARM pulse with amplitude 2A typicallyachieves a second harmonic mean level only ∼−6 dB belowthe second harmonic of the undistorted transmitted pulseover a depth that reduces with an increase in MI.

Second, the use of larger aperture transducers enablesfocusing at longer depths with lower f-numbers and simul-taneously allows for higher MIs. In Fig. 5, we show thespectral content up to 4.5 MHz of a clipped HARM pulsegenerated from a 40-mm diameter circular aperture withf-number 2.5. The forward propagation of a 2-MHz pulseof twice the amplitude of the transmit pulse used to gen-erate the HARM pulse produces a MI = 1.1 in the focalregion for f-number 2.5 in liver. The ringing associatedwith Gibbs phenomenon is apparent in the time-domainwaveform. This can be eliminated by more sophisticatedwindowing to narrow the bandwidth.

C. HARM Pulses in Layered Medium

A simple, two-layer model consisting of fat and livercan be used to represent the abdomen. The fat layer varies

Fig. 5. A 40-mm diameter transducer focused at 10 cm, 2 MHzclipped HARM pulse in liver f-number 2.5. (a) Spectral composition.(b) Waveform.

Fig. 6. A 25-mm diameter transducer focused at 10 cm depth. Ax-ial propagation of the second harmonic of high amplitude 2 MHzGaussian (––) and clipped 2 MHz HARM (----) pulse normalizedwith respect to the fundamental at f-number 4 in layered mediumat MI∼0.45. (a) 2-cm fat and 14-cm liver at twice the amplitude.(b) 4-cm fat and 12-cm liver at three times the amplitude. HARMharmonics are < −25 dB with respect to the fundamental over a4-cm depth.

from 2 to 4 cm, followed by the liver layer varying from 14to 12 cm. Fat is characterized by a higher nonlinearity pa-rameter of 6.5 and a higher attenuation coefficient of 0.15compared to liver. The signal simultaneously attenuates infat and accumulates harmonic energy in proportion to thelayer thickness. In order to perform imaging at high MI,clipped liver HARM pulses of higher amplitude are usedto minimize harmonics that are generated during acousticwave propagation through the layered media.

The forward propagation profile for a a 2-cm fat layerfollowed by a 14-cm liver layer at twice the amplitude andfor a 4-cm fat layer followed by a 12-cm liver layer at threetimes the amplitude of Gaussian and clipped HARM pulsesat a MI of 0.45 for f-number 4 is presented in Fig. 6(a) and(b), respectively. The lower MIs in the focal region of thelayered medium compared to those in liver is related to thestronger attenuation of the sound beam in the fat layer.

We also have used the HARM pulse shown in Fig. 5at twice its amplitude to minimize harmonics generatedby a high amplitude 2 MHz pulse focused at 10-cm depthfrom a circular aperture of 40 mm. Effective aperture maybe increased through a larger half-width at half maximum

252 ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 55, no. 1, january 2008

Fig. 7. A 40-mm diameter transducer focused at 10-cm depth. Axialpropagation of the second harmonic of high amplitude 2 MHz Gaus-sian pulse (––) and clipped 2 MHz liver HARM (----) pulse withrespect to the fundamental in layered media of 2-cm fat and 14-cmliver for 4-number 2.5 for two apodization weights. (a) MI = 0.7.(b) MI = 0.85. Note that HARM harmonics are < −25 dB withrespect to the fundamental over a 4-cm depth.

(HWHM) in the Gaussian apodization to achieve a higherMI. The forward propagation of the second harmonic ofhigh amplitude 2 MHz Gaussian pulse and a clipped liverHARM pulse in a layered medium consisting of 2-cm fatand 14-cm liver for two apodization functions is shown inFigs. 7(a) and (b). The high amplitude pulse from a largereffective aperture achieves a MI = 0.85 marking an 89%increase over a corresponding high amplitude pulse froman aperture with a 37.5% smaller physical radius that isshown in Fig. 6(a).

IV. Discussion

We have simulated HARM pulses in liver medium for atransmit frequency of 2 MHz with a 50% bandwidth, 25-mm circular aperture. Though computed HARM pulsesare very wide-band, the additional second harmonic com-ponent is adequate to achieve a minimization level <−25 dB. The use of larger diameter apertures and largereffective apertures created by wider apodization resultsin extending the capability of the algorithm to producehigher MI pulses from the same focal depth. We have beenable to generate HARM pulses with MI up to 1.1 at a depthof 10 cm in a homogeneous liver-like medium.

These findings have been applied in a representativeabdominal medium modeled by a varying layer of fat (2–4 cm) and liver (14–12 cm). Liver HARM pulses can beused to perform contrast imaging for difficult-to-image pa-tients by adjusting the amplitude of the pulse and apodiza-tion function. We have been able to generate up to aMI = 0.85 in layered medium with 2-cm fat with a combi-nation of larger diameter and wider effective aperture witha high amplitude predistorted pulse.

Suppression of second harmonics for larger aperturesand lower f-numbers had been reported earlier by Krish-nan et al. in the context of the forward nonlinear propa-gation of the original transmit waveform [2]. Our analy-sis validates their observations for predistorted waveformsas well. Christopher [4] had used scale factors on the

second harmonic content of the prebiased transmit waveto achieve improved sidelobe suppression of predistortedtransmit waveforms in inhomogeneous medium. We usedscale factors for the entire HARM waveform to achievehigher MIs.

V. Conclusions

Our study has multiple limitations. Our method isaimed at minimizing the second harmonic in the axial di-rection. In practice, harmonics need to be minimized inboth axial and radial directions. Christopher’s [4] scaledpredistorted pulses had an inherent side-lobe advantagein inhomogeneous medium. We need to ensure that ourmethod has a similar advantage. We do not explicitlymodel the phase aberration across the fat and liver in-terface. Our simulations also assume normal incidence ofultrasound, thereby ignoring refractive effects between thetwo layers. Our approach would imply the need for pre-liminary scans to assess the thickness of the fat layer todesign a feedback mechanism to scale the original trans-mit waveform or alter the aperture apodization to correctfor the second harmonic. The use of scale factors leads toincomplete minimization as shown in Figs. 4(a) and (b),6(a) and (b), and 7(a) and (b). As a consequence, theremay be limited advantage in high MI contrast imagingwith HARM pulse.

Designing customized pulses for difficult-to-image pa-tients could be challenging. Therefore, if fat could betreated as a layer of variable thickness, it may be usefulto perform abdominal imaging with liver HARM pulse tosimultaneously achieve high MIs and minimize tissue har-monics. The methodology could be extended to maximizeharmonics due to tissue propagation over large depths inthe absence of contrast agents.

Our simulations have been based on an aperture withcircular geometry. However, the method is generic andcould be expected to be applicable to rectangular aper-tures as well.

Our next steps are aimed at designing patient-independent HARM pulses that can be implemented in aclinical setting and verifying the findings reported in thiscorrespondence through experiments with cMUT annulararray transducers and tissue-mimicking phantoms.

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