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Imaging Parameters on Third Harmonic Transmit Phasing for Tissue Harmonic Generation
Ultrasound in Med. & Biol., Vol. 34, No. 6, pp. 1001–1013, 2008 Copyright © 2008 World Federation for Ultrasound in Medicine & Biology Printed in the USA. All rights reserved 0301-5629/08/$–see front matter
doi:10.1016/j.ultrasmedbio.2007.12.001
● Technical Note IMAGING PARAMETERS ON THIRD HARMONIC TRANSMIT PHASING FOR 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 and 3f0 signal are used to generate both frequency-sum and frequency-difference components for manipulation of tissue harmonic amplitude. Nevertheless, the acoustic propagation of 3f0 transmit signal suffers from more severe attenuation 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 transmit phasing. In this study, extensive simulations were performed to investigate the effects of these imaging parameters. Results indicate that the harmonic enhancement and suppression in 3f0 transmit phasing are compromised when the magnitude of frequency-difference component decreases in the presence of tissue attenuation and phase aberration. To compensate for the reduced frequency-difference component, a higher 3f0 transmit amplitude can be used. When the transmit parameters are concerned, a smaller 3f0 transmit aperture can provide more axially uniform harmonic enhancement and more effective suppression of harmonic amplitude. In addition, the spectral leakage signal also interferes with tissue harmonics and degrades the efficacy of 3f0 transmit phasing. Our results suggest that, in the method of 3f0 transmit phasing, the transmit amplitude, phase and aperture size of 3f0 signal should remain adjustable for optimization of clinical performance. Besides, multipulse sequences such as pulse inversion 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.
improves, especially on technically difficult bodies (Christopher 1997, 1998; Tranquart et al. 1999; Desser and Jeffrey 2001). Even with aforementioned advantages, imaging with tissue harmonic signal suffers from several difficulties. For example, under typical imaging conditions, only a small amount of harmonic signal is generated during the acoustic propagation and thus both penetration and sensitivity of tissue harmonic imaging are limited because of the lower signal-to-noise ratio (Li 1999). On the contrary, in contrast agent harmonic imaging, where microbubbles are routinely used to enhance image contrast between blood-perfused areas and tissue background, the presence of tissue harmonics may obstruct the detection of microbubble contrast agents and degrade the contrast-to-tissue ratio (CTR), especially when a higher mechanical index is adopted (Burns 1996; Chang et al. 1996; de Jong and Ten Cate 1996). Because both enhancement and suppression of tissue harmonic amplitude are essential, respectively, for tissue and contrast
INTRODUCTION Tissue harmonic signal from finite amplitude distortion of propagating sound wave is generally characterized as progressive steepening of the waveform as a result of the pressure-dependent acoustic velocity in nonlinear medium (Beyer and Letcher 1969; Haran and Cook 1983; Cain 1986). Because the tissue harmonics build up gradually with distance from the transducer, the ultrasound signal at harmonic frequency is relatively weak in the beginning of propagation. Consequently, reverberation from shallow structures such as interfaces between skin and fat can be markedly suppressed because of the low echo intensity. Besides, sidelobes of the nonlinearly generated beam are much lower than those of the linear beam and the corresponding image contrast significantly Address correspondence to: Che-Chou Shen, Department of Electrical Engineering, National Taiwan University of Science and Technology, #43, Sec.4, Keelung Rd., Taipei, 106, Taiwan. E-mail: [email protected] 1001
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imaging, there have been various techniques proposed to manipulate the tissue harmonic amplitude (Lu and Greenleaf 1991; Krishnan et al. 1998; Christopher 1999; Li and Shen 1999; Zhou and Hossack 2003; Chiao and Hao 2005). We have recently presented a novel method to change the tissue harmonic amplitude: the third harmonic (3f0) transmit phasing (Shen et al. 2007). The proposed method is based on transmitting an additional 3f0 signal together with the original fundamental signal (f0) to modify the tissue harmonic amplitude. During the nonlinear propagation in tissue, new spectral components will be generated at the sum and difference frequencies of the original transmit signals. These tissue harmonic signals are referred to as the frequency-sum component and the frequency-difference component, respectively. In conventional tissue harmonic imaging, the second harmonic signal is dominated by the frequency-sum component, which comes from the multiplication of the f0 signal with itself. Nevertheless, the frequency-difference component of second harmonic signal can also be produced from the spectral interaction between the f0 signal and the 3f0 signal when the transmit waveform consists of both signals. Note that the phase of the frequency-sum component of second harmonic signal is proportional to 2f when the fundamental transmit signal is modeled as exp(j(2f0t⫹f)). The symbol f is the phase of the f0 transmit signal. On the other hand, the frequency-difference component is related to both phases of the f0 and 3f0 transmit signals. Specifically, the phase of frequencydifference component will be provided that the 3f0 transmit signal is modeled as exp(j(2(3f0)t⫹⫹f)). The symbol represents the relative phase between the 3f0 transmit signal and the f0 transmit signal. Consequently, tissue harmonic generation can be enhanced when the two components are in-phase and being constructively summed together. Otherwise, they may cancel out each other and result in reduced tissue harmonic amplitude. In other words, the phase relation between the frequency-sum and the frequency-difference component should be ⫽ 2 f ⫹ for second harmonic suppression, whereas the relation ⫽ 2 f leads to enhancement of second harmonic amplitude. The previously mentioned two phase relations suggest that the manipulation of second harmonic amplitude can be achieved by simply tuning the 3f0 transmit phase. The 3f0 transmit phasing is very different from other approaches that simultaneously transmit two frequencies. For example, in differential tissue harmonic imaging (DTHI) from Toshiba, transmission at both f0 and 2f0 frequencies is used for additional differential harmonic signal at f0 frequency (US Patent 2005; Nowicki et al. 2007). Note that there is not spectral overlap between the
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differential harmonic signal and the second harmonic signal and, hence, the resultant harmonic amplitude does not rely on the relative phasing between transmit signals. In 3f0 transmit phasing, generation of frequencydifference component involves the 3f0 transmit signal and thus, both the axial and lateral characteristics of the frequency-difference component depend on those of the constitutive 3f0 beam. Compared with the f0 signal, the focusing of 3f0 signal is typically stronger and the acoustic power is more concentrated in the axial and lateral directions. Since the same acoustic power can be delivered to the focal zone with lower transmit amplitude at 3f0 frequency due to its stronger focusing, the amplitude of 3f0 transmit signal can be lower than the f0 transmit amplitude while the generation of frequency-sum and frequency-difference components are still approximately equal in magnitude for maximal cancellation of these two signals. For example, with the same aperture size at both f0 and 3f0 frequencies, the optimal transmit amplitude ratio of the 3f0 signal to the f0 signal is about 0.5 for harmonic suppression (Shen et al. 2007). In other words, for example, the transmit amplitude of the 3f0 signal would be about 100 kPa for maximal harmonic suppression when the corresponding f0 transmit amplitude is 200 kPa. Nevertheless, because the 3f0 transmit phasing utilizes transmission at higher frequency, its performance would vary with imaging parameters that are sensitive to frequency. In this technical note, relevant imaging parameters in 3f0 transmit phasing are investigated using simulations. This paper is organized as follows. First, the selection of relevant imaging parameters is described together with the simulation model. These imaging parameters are divided into two categories: tissue parameters and transmit parameters, and their effects are individually considered. Finally, conclusions and discussions of this study will be given. METHODS Selection of relevant imaging parameters Because the 3f0 transmit phasing relies on the frequency-difference component to achieve either constructive enhancement or destructive cancellation of the tissue harmonic signal, the beam properties of frequency-difference component would inevitably change the performance of 3f0 transmit phasing. There are several imaging parameters that could significantly change the frequencydifference component and thus result in degradation of 3f0 transmit phasing. For example, the frequency-dependent attenuation in biological tissues would markedly reduce the amplitude of 3f0 signal relative to that of the f0 signal during the acoustic propagation. Consequently, as compared with the frequency-sum component, the
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amplitude of frequency-difference component could severely decrease such that the efficacy of harmonic enhancement and suppression is limited. Another frequency-dependent tissue parameter is phase aberration. With fixed time delay error in transmit/receive channels because of tissue inhomogeneities, the corresponding phase error increases with frequency and, hence, results in more deteriorated beam at higher frequency. Consequently, the divergent 3f0 beam may also degrade the performance of 3f0 transmit phasing. In addition to those aforementioned tissue parameters, transmit parameters such as the aperture size of 3f0 transmit signal also play important roles in 3f0 transmit phasing. In enhancement mode, we have shown previously that the depth of focus of the tissue harmonic signal would become shorter because of the strong focusing of the frequency-difference component (Shen et al. 2007). Consequently, the SNR in harmonic imaging may deteriorate rapidly for off-focus region. To elongate the depth of focus in 3f0 transmit phasing, a smaller 3f0 transmit aperture can be used to generate a frequencydifference beam with longer depth of focus. The 3f0 aperture size can be readily modified in an array system by changing the number of transmit channels. Besides, when a wideband pulse is transmitted for better axial resolution, the effect of harmonic leakage cannot be ignored. The linearly propagated harmonic leakage signal has higher sidelobes than its nonlinear counterpart and thus compromises the image contrast in tissue harmonic imaging (Shen and Li 2001). The leakage signal also increases the harmonic amplitude in tissue background and hence reduces the specificity of contrast agents in harmonic imaging (Krishnan and O’Donnell 1996). Similarly, in 3f0 transmit phasing, the presence of leakage signal could also deteriorate the efficacy of tissue harmonic suppression and cause difficulties in the detection of contrast harmonic signal. Based on these observations, relevant imaging parameters including attenuation, phase aberration, 3f0 transmit aperture size and transmit signal bandwidth are considered for their effects on 3f0 transmit phasing in this study. Simulation model In the simulation model, the transmit waveform is first decomposed into discrete temporal frequency components. For each frequency component, continuous beam formation is approximated by incremental field propagation. At each increment, linear propagation is simulated based on the angular spectrum method (Goodman 1968; Liu and Waag 1997). The nonlinear propagation is modeled using the finite amplitude distortion model (Christopher 1997). As shown in the following
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equation, the finite amplitude distortion model utilizes the frequency domain solution to Burgers’ equation, i.e.
un ⫽ u⬘n ⫹ j
 f⌬z 2c2
冋兺
n⫺1
N
ku⬘ku⬘n⫺k ⫹
k⫽1
兺 nu u
⬘ ⬘ k k⫺n
k⫽n
*
册
(1)
In eqn (1), ⌬z is the propagation increment along the axial direction. The fundamental frequency is denoted by f and  is a parameter representing the nonlinearity of the propagation medium. The term u⬘n denotes the temporal velocity field at frequency nf (n is an integer) after linear propagation. Likewise, un denotes the temporal velocity field after nonlinear propagation. The sound velocity is denoted by c. A one-dimensional, 64-channel linear array is assumed to transmit the 2-MHz fundamental signal together with the corresponding 3f0 signal at 6 MHz. The array had a 0.3-mm pitch and the transmit focus was set to 55 mm away from the transducer. The propagation medium was assumed to be homogeneous unless particularly specified and the nonlinear parameter  was set to 3.5, approximating the nonlinear property of water (Law et al. 1985). For simplicity, frequency response of the transducer is ignored without loss of generality. In the simulation model, transmit signals of either continuous wave (CW) or pulse wave (PW) can be adopted. For a CW case, the harmonic signals are represented as the corresponding Fourier series of the transmit waveform. For a PW case, the simulated second harmonic signal is extracted by band-pass filtering, with a flat frequency response between 3 MHz and 5 MHz. For both CW and PW transmit, the peak acoustic pressure at fundamental frequency is 200 KPa. For the 3f0 transmit signal, its acoustic pressure is determined by the 3f0 amplitude ratio and its phase can be changed from –170° to 180°. RESULTS Effects of tissue parameters Attenuation. CW simulations were performed to study the effect of frequency-dependent attenuation on 3f0 transmit phasing. Attenuation coefficients ␣ of 0.02, 0.06 and 0.11 np/cm/MHz were considered, which correspond to the attenuation in blood, fat and liver tissues, respectively (Shung et al. 1992). The simulated second harmonic axial amplitudes, lateral beam patterns and the corresponding integrations of beam pattern are demonstrated with ␣ ⫽ 0.06 np/cm/MHz in Fig. 1d–f, respectively. For comparison, corresponding results without attenuation (i.e., ␣ ⫽ 0 np/cm/MHz) are also illustrated in Fig. 1a– c, respectively. In these simulations, the amplitude ratio of 3f0 transmit signal is fixed at 0.5. In Fig. 1a and d, the axial amplitudes of both enhancement mode
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Fig. 1. Simulated second harmonic axial amplitudes, beam patterns and integrated beam patterns with different ␣ values. Left: ␣ ⫽ 0 np/cm/MHz. Right: ␣ ⫽ 0.06 np/cm/MHz.
and suppression mode are normalized to the focal amplitude without 3f0 transmit for each ␣ value. In other words, the normalized amplitude will be larger than unity if the 3f0 transmit signal results in enhancement of harmonic amplitude. Otherwise, the suppression of harmonic generation will make the normalized amplitude less than unity. Figure 1d shows that, after attenuation, the 3f0 transmit phasing is still effective for both enhancement and suppression of second harmonic signal over a wide range of axial depths. However, it should be noted that the performance of 3f0 transmit phasing is degraded compared with that without attenuation. Specifically, the focal enhancement is reduced from about 6 dB without attenuation to only 3 dB with ␣ ⫽ 0.06 np/cm/MHz. The corresponding focal suppression is also reduced from about 11 dB without attenuation to only 6 dB with ␣ ⫽ 0.06 np/cm/MHz. In other words, when tissue attenuation is considered, 3f0 transmit phasing results in less change of second harmonic amplitude. Similar observations can be made from the beam patterns. In Fig. 1b and e, the focal beam patterns are normalized to the on-axis amplitude without 3f0 transmit for each ␣ value. Specifically, without tissue attenuation, the beam pattern of enhancement mode is more concentrated (i.e., lower sidelobes and narrower mainlobe) such that the corresponding lateral and contrast resolution are superior to that without 3f0 transmit. Nevertheless, after tissue attenuation, the radiation patterns of both enhancement and suppression modes become more similar to that without 3f0 transmit. Although the enhancement beam
still has lower sidelobes, the improvement of image quality has been compromised because of attenuation. The integrated beam patterns in Fig. 1c and f also reveal that the profiles tend to be more close to each other when the attenuation is present. The variation of second harmonic amplitude with 3f0 transmit phase at focal depth is also shown in Fig. 2. For each ␣ value, the focal second harmonic amplitudes are normalized to that without 3f0 transmit signal. It is clearly demonstrated that the extent of enhancement and suppression using 3f0 transmit phasing decreases with the attenuation. The results are as expected because a smaller amount of frequency-difference component would be generated at second harmonic frequency when its constitutive 3f0 transmit beam suffers from severe attenuation during propagation. However, it is also noticeable in Fig. 2 that the 3f0 transmit phases for maximal enhancement and suppression are insensitive to tissue attenuation. For example, the 3f0 transmit phase for maximal suppression only slightly drifts from – 60° to – 40° when the ␣ increases from 0 np/cm/MHz to 0.11 np/cm/MHz. Because the magnitude of 3f0 transmit beam is markedly reduced in the presence of attenuation and thus produces insufficient frequency-difference component, the 3f0 transmit amplitude at source should be increased to compensate the attenuated frequency-difference component. Figure 3 shows the focal second harmonic amplitudes as a function of 3f0 transmit amplitude ratio with different attenuations. It is demonstrated that the 3f0 transmit amplitude ratio for optimal suppression obviously increases with attenuation. For example, the 3f0
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Fig. 2. Simulated focal second harmonic amplitudes as a function of 3f0 transmit phase with different ␣ values. The 3f0 transmit amplitude ratio is fixed at 0.5.
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 be ignored, a higher 3f0 transmit amplitude is required to compensate the signal loss of frequency-difference component for better harmonic suppression. In addition, it should be noted that the harmonic enhancement would also benefit from the stronger 3f0 transmit signal.
Phase aberration In this study, PW simulations were performed to investigate the effect of phase aberration on 3f0 transmit phasing. In the simulations, a displaced phase screen was included to model sound velocity variations between two different media. Such a model is similar to the one proposed in Liu and Waag (1994). The medium next to the transducer had a propagation velocity of 1.45 mm/s,
Fig. 3. Simulated focal second harmonic amplitudes as a function of 3f0 transmit amplitude with different ␣ values. The 3f0 transmit phase is fixed at suppression mode.
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Fig. 4. Pattern of time delay error for 4⫻ aberration. Positive phase shift is displayed in white and the negative shift is in black.
a uniform thickness of 15 mm and a  of 6 to mimic the nonlinear properties of fat tissue (Law et al. 1985). The deeper medium is assumed to be water with a thickness of 65 mm. Time delay errors resulting from irregular thickness of fat tissue were simulated using a 2-D phase screen at the boundary of the two media. The phase screen had a correlation length of 5 mm and can be scaled to include different extent of phase error. For convenience, the phase screens with root-mean-square (RMS) time delay error of 11.6, 23.3 and 46.6 ns are referred to as 1⫻ aberration, 2⫻ aberration and 4⫻ aberration, respectively, in this paper. Gray level image of the 4⫻ aberration pattern is shown in Fig. 4. Figure 5a and c show the beam patterns at focal depth without aberration and with 4⫻ aberration, respec-
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tively. Note that the corresponding 46.6-ns RMS time delay error with the 4⫻ aberration is relatively large compared with those measured in biological tissue (Hinkelman et al. 1994, 1995) and thus significant beam distortion is expected. Compared with the case in homogeneous tissue, the beam patterns with phase aberration are markedly distorted and the resultant sidelobe levels are elevated for both enhancement and suppression. Similar observations can be made using the integrated beam patterns in Fig. 5b and d. The profile of enhancement mode converges to unity much slower compared with its no-aberration counterpart. It is also shown that, unlike the distinct difference among integration profiles without aberration, the profile of harmonic enhancement becomes similar to that without 3f0 transmit when the aberration is present. In other words, the beam quality of second harmonic signal in 3f0 transmit phasing is significantly degraded by phase aberration. The variation of focal second harmonic amplitude as a function of 3f0 transmit phase is also demonstrated using simulations in Fig. 6 with different aberrations. For each aberration, the second harmonic amplitudes with 3f0 transmit are normalized to that without 3f0 transmit. Figure 6 shows that both enhancement and suppression of second harmonic amplitude tend to be compromised when the phase error increases. It is also shown, however, that the presence of phase aberration does not result in significant change of 3f0 transmit phase for either harmonic enhancement or suppression. For example, the maximal harmonic suppression without aberration is
Fig. 5. Simulated second harmonic beam patterns and integrated beam patterns without (left) and with 4⫻ aberration (right).
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Fig. 6. Simulated focal second harmonic amplitudes as a function of 3f0 transmit phase with different aberrations. The 3f0 transmit amplitude ratio is fixed at 0.5.
achieved with a 3f0 transmit phase of 120°. When the 4⫻ aberration is included, the 3f0 transmit phase for maximal harmonic suppression slightly drifts to 140°. In other words, although the presence of phase aberration reduces the efficacy of both harmonic enhancement and suppression, the corresponding 3f0 transmit phase remains relatively unchanged. Effects of transmit parameters 3f0 transmit aperture size. In this study, the relative size of 3f0 aperture to the fundamental aperture is considered using CW simulations. In Fig. 7, the focal second harmonic amplitudes are represented as a function of both amplitude ratios and phases of 3f0 transmit signal. The 3f0 aperture sizes are 100%, 75% and 50% of the fundamental aperture size, respectively, in Fig. 7a– c. Note that, for example, the 50% 3f0 aperture uses the central 32 channels for transmit, whereas the fundamental aperture comprises the whole 64 channels. The focal second harmonic amplitudes in Fig. 7 have been normalized to that without 3f0 transmit for each 3f0 aperture and the gray bar in each panel maps the normalized harmonic amplitudes into gray levels. In Fig. 7a, it is apparent that the most effective suppression of second harmonic signal with the 100% 3f0 aperture is achieved when the 3f0 transmit amplitude ratio is scaled to about 0.45. Nevertheless, it is shown in Fig. 7b and c that the maximal harmonic suppression occurs with a higher 3f0 transmit amplitude when a smaller 3f0 aperture is used. For example, the optimal ratios for harmonic suppression change to 0.55 and 0.8,
respectively, for the 75% and 50% 3f0 apertures. The increase of 3f0 transmit amplitude ratio is as expected because a higher amplitude is necessary to maintain similar 3f0 transmit energy with a reduced aperture size. For all figures, it is also obvious that the harmonic enhancement monotonically increases with the 3f0 transmit amplitude. Moreover, the 3f0 transmit phases corresponding to harmonic enhancement and suppression do not change with different aperture sizes. For example, the 3f0 transmit phase for harmonic suppression remains at – 60° when the 3f0 aperture decreases from 100% to 50%. The second harmonic axial amplitudes and the lateral beam patterns in enhancement mode are shown in Fig. 8a and b for different 3f0 apertures. Note that, in both Fig. 8 and Fig. 9, different 3f0 transmit amplitudes are selected for different apertures based on the results in Fig. 7 to achieve maximal suppression of harmonic amplitude. When the 3f0 aperture size is reduced from 100% to 75% and 50%, the corresponding second harmonic amplitudes become more uniformly distributed in the axial direction and thus provide longer depths of focus. Nevertheless, it should be noted that the long depth of focus is achieved at the cost of image quality. As shown in Fig. 8b, for a smaller 3f0 aperture, the mainlobe becomes wider and the sidelobe levels are also elevated. Consequently, the image resolution and image contrast can be compromised because of the less directive beam. In suppression mode, the 3f0 transmit aperture also play an important role to optimize the harmonic suppression in both axial and lateral directions. As shown in Fig.
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Fig. 7. Simulated focal second harmonic amplitudes as a function of 3f0 transmit phase and 3f0 transmit amplitude ratio with different 3f0 transmit aperture sizes. From left to right: 100%, 75% and 50%, respectively.
9a, although similar harmonic suppression at focal depth can be achieved with different sizes of 3f0 apertures, the prefocal and postfocal second harmonic amplitudes become elevated with a reduced 3f0 aperture size. In the extreme case of 50% 3f0 aperture, the harmonic suppression is effective only at focal depth. Nevertheless, it is noticeable that the 75% 3f0 aperture not only provides effective harmonic suppression for a wide range of axial depths, the corresponding radiation pattern in Fig. 9b also has the lowest magnitude in the mainlobe region compared with the other two apertures. In other words, harmonic suppression with the 75% 3f0 aperture is effective over a larger range in both axial and lateral directions such that the tissue background in contrast imaging can be better suppressed. Transmit bandwidth In 3f0 transmit phasing, the presence of leakage harmonic signal would interfere with the frequency-sum and the frequency-difference components of tissue harmonic signal. PW simulations were performed to illustrate two different conditions of spectral leakage in 3f0 transmit phasing. Condition I occurs when the transmit signals at both f0 and 3f0 frequencies are wideband pulses such that the leakage signals come from both the fundamental transmit band and the 3f0 transmit band. Specifically, the transmit signal is a Gaussian pulse with a – 6 dB bandwidth of about 1.6 MHz at both f0 and 3f0
frequencies, which contains considerable spectral energy at second harmonic band. In Condition II, however, the bandwidth of the 3f0 transmit signal is reduced to about 0.6 MHz to avoid spectral leakage from the 3f0 transmit band. In other words, the f0 transmit pulse is wideband and the 3f0 transmit pulse is narrowband in Condition II. For Condition I shown in Fig. 10a– c, although the harmonic suppression mode still provides lower axial amplitudes than the enhancement mode, it should be noted that the second harmonic amplitudes are already higher than those without 3f0 transmit for all depths because of the additional leakage signal from the 3f0 transmit band. Consequently, the 3f0 transmit phasing does not provide any tissue suppression compared with the case without 3f0 transmit and, hence, no CTR improvement is expected in contrast harmonic imaging. For harmonic enhancement, the increase of harmonic amplitude is also reduced from 6 dB to about 3 dB in the presence of spectral leakage. It is also shown that the sidelobes of all beam patterns are markedly elevated because of the leakage signal such that all integration profiles converge slowly and become less distinguishable as compared with Fig. 5b, where no spectral leakage is considered. For Condition II, however, only spectral leakage from the fundamental band is present because the narrowband 3f0 transmit pulse produces negligible leakage signal. As shown in Fig. 10d, the second harmonic amplitude at source in both enhancement and suppression mode is equal to that
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Fig. 8. (a) Simulated second harmonic axial amplitudes with different 3f0 transmit aperture sizes. The 3f0 transmit phase is fixed at enhancement mode. (b) Simulated second harmonic beam patterns with different 3f0 transmit aperture sizes.
without 3f0 transmit. Accordingly, the tissue harmonic amplitude can be better suppressed as the sound wave propagates. Furthermore, when the harmonic enhancement is considered, the beam quality of tissue harmonic signal is apparently superior to that without 3f0 transmit and, hence, the corresponding integration profile in Fig. 10f rises more rapidly than others. Nevertheless, although the 3f0 transmit phasing performs better in Condition II, it should be noted that the sidelobes in enhancement beam is still much higher compared with those without leakage (i.e., in Fig. 5a) and thus the loss of contrast resolution in tissue harmonic imaging is inevitable. In addition, the presence of leakage
signal increases harmonic amplitudes, especially in the near field and, hence, the efficacy of harmonic suppression in 3f0 transmit phasing is still limited in Condition II. DISCUSSION Although this study is performed without presenting real ultrasound images, information about possible variation of image quality in 3f0 transmit phasing has been provided without loss of generality by comparing the simulated acoustic beams. In the simulations, it is assumed that the dispersion effect characterized as varia-
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Fig. 9. (a) Simulated second harmonic axial amplitudes with different 3f0 transmit aperture sizes. The 3f0 transmit phase is fixed at suppression mode. (b) Simulated second harmonic beam patterns with different 3f0 transmit aperture sizes.
tion of sound velocity with frequency is negligible. Nevertheless, the dispersion could lead to different distortion of the f0 and 3f0 beams and further degrade the method of 3f0 transmit phasing. Therefore, adequate time delay correction can be applied at the transmit part of the imaging system so as to avoid severe distortion of 3f0 transmit beam and the corresponding frequency-difference signal. Results also indicate that tissue characteristics such as frequency-dependent attenuation and tissue inhomogeneities can result in significant decrease of the magnitude of 3f0 signal during propagation. Consequently, the achievable harmonic enhancement and sup-
pression are also reduced because of the lower frequency-difference magnitude in the presence of tissue attenuation and phase aberration. To compensate for the magnitude loss of 3f0 signal during propagation, a higher transmit amplitude at 3f0 frequency can be used to generate sufficient frequency-difference component so as to cancel with the frequency-sum component for maximal harmonic suppression. The higher transmit amplitude at 3f0 frequency is also necessary in the case of a smaller 3f0 aperture. Because the 3f0 transmit phasing is sensitive to the parameters of propagation tissue, which cannot be
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Fig. 10. Simulated second harmonic axial amplitudes, beam patterns and integrated beam patterns with different conditions of spectral leakage. Left: Condition I. Right: Condition II.
known in advance, the optimal phase and amplitude of 3f0 transmit signal could vary significantly in different clinical applications. Consequently, imaging calibration is required to select these 3f0 transmit parameters. This kind of calibration can be performed automatically by measuring the tissue harmonic amplitudes with different combinations of 3f0 transmit amplitude and phase. For example, the 3f0 transmit amplitude and phase that result in the lowest tissue harmonic amplitude should be used for harmonic suppression in that particular condition. Moreover, it should be noted that the 3f0 transmit phase that corresponds to the enhancement or suppression of tissue harmonic signal is quite invariant to tissue parameters. This phenomenon 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 bandwidth at either f0 or 3f0 frequencies markedly degrades the harmonic enhancement and suppression. Nevertheless, the limitation can be avoided when the multipulse transmit scheme such as pulse inversion (PI) is adopted to remove the leakage signal (Simpson et al. 1999; Shen and Li 2002). The PI technique involves two firings with inverted waveforms for each acoustic beam line. When the returning echoes from the two firings are summed, the linearly propagated leakage signal is cancelled and only nonlinearly generated 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 the PI technique can restore the contrast resolution in tissue harmonic imaging by providing much lower sidelobes than those without PI technique. CONCLUSIONS In this paper, the performance of 3f0 transmit phasing on tissue harmonic generation is studied with various imaging parameters. It is demonstrated that the 3f0 transmit signal is susceptible to tissue parameters such as tissue attenuation and beam distortion during acoustic propagation. Consequently, in clinical applications of 3f0 transmit phasing, imaging calibration is suggested to determine the optimal phase and amplitude of the 3f0 transmit signal. It is also shown that the transmit parameters such as aperture size and bandwidth significantly change the tissue harmonic generation in 3f0 transmit phasing. Compared with using the same aperture size for both f0 and 3f0 transmit, a smaller 3f0 aperture can provide more effective harmonic suppression over a larger region in both axial and lateral directions for contrast harmonic imaging. With imaging parameters used in this study, the optimal 3f0 transmit aperture for harmonic suppression is about 75% of the f0 aperture size. When harmonic enhancement is concerned in tissue harmonic imaging, a smaller 3f0 aperture is also favorable when more uniform
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Fig. 11. Simulated second harmonic beam patterns without and with the PI technique. The 3f0 transmit phase is fixed at enhancement mode.
harmonic amplitudes in the axial direction are preferred for longer depth of focus. The selection of transmit bandwidth at both f0 and 3f0 frequencies also markedly change the efficacy of 3f0 transmit phasing on harmonic enhancement and suppression. When the wideband transmit pulses are used for better axial resolution, the spectral leakage signal degrades the beam quality in tissue harmonic imaging with decreased harmonic enhancement. On the other hand, the leakage signal also reduces the achievable suppression of tissue background in contrast harmonic imaging. Therefore, removal of spectral leakage signal using multipulse transmit scheme such as PI technique is beneficial in 3f0 transmit phasing. Acknowledgments—Supported in part by the National Science Council of Taiwan under grant NSC 96-2221-E-011-143 and Intelligent Building Research Center of National Taiwan University of Science and Technology are gratefully acknowledged. We also thank the reviewers for the helpful comments.
REFERENCES Beyer RT, Letcher SV. Nonlinear Acoustics. New York: Academic, 1969. Burns PN. Harmonic imaging with ultrasound contrast agents. Clin Radiol 1996;51(Suppl 1):50 –55. Cain CA. Ultrasonic reflection mode imaging of the nonlinear parameter B/A. I: A theoretical basis. J Acoust Soc Am 1986;80:28 –32. Chang PH, Shung KK, Levene HB. Quantitative measurements of second harmonic Doppler using ultrasound contrast agents. Ultrasound Med Biol 1996;22:1205–1214. Christopher T. Finite amplitude distortion-based inhomogeneous pulse echo ultrasonic imaging. IEEE Trans Ultrason Ferroelectr Freq Control 1997;44:125–139.
Christopher T. Experimental investigation of finite amplitude distortion-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 bubble-response imaging. IEEE Trans Ultrason Ferroelectr Freq Control 1999;46:556 –563. Chiao RY, Hao X. Coded excitation for diagnostic ultrasound: a system developer’s perspective. IEEE Trans Ultrason Ferroelectr Freq Control 2005;52:160 –170. de Jong N, Ten Cate FJ. New ultrasound contrast agents and technological innovations. Ultrasonics 1996;34:587–590. Desser TS, Jeffrey RB. Tissue harmonic imaging techniques: Physical principles and clinical applications. Semin Ultrasound CT MR 2001;22:1–10. Goodman JW. Introduction to Fourier Optics. New York: McGrawHill, 1968. Haran ME, Cook BD. Distortion of finite amplitude ultrasound in lossy media. J Acoust Soc Am 1983;73:774 –779. Hinkelman LM, Liu DL, Metlay LA, Waag RC. Measurements of ultrasonic pulse arrival time and energy level variations produced by propagation through abdominal wall. J Acoust Soc Am 1994; 95:530 –541. Hinkelman LM, Liu DL, Waag RC, Zhu Q, Steinberg BD. Measurement and correction of ultrasonic pulse distortion produced by the human breast. J Acoust Soc Am 1995;97:1958 –1969. Krishnan S, Hamilton JD, O’Donnell M. Suppression of propagating second harmonic in ultrasound contrast imaging. IEEE Trans Ultrason Ferroelectr Freq Control 1998;45:704 –711. Krishnan S, O’Donnell M. Transmit aperture processing for nonlinear contrast agent imaging. Ultrason Imaging 1996;18:77–105. Law WK, Frizzell LA, Dunn F. Determination of the nonlinearity parameter B/A of biological media. Ultrasound Med Biol 1985;11: 307–318. Li PC. Pulse compression for finite amplitude distortion based harmonic imaging using coded waveforms. Ultrason Imaging 1999; 21:1–16. Li PC, Shen CC. Effects of transmit focusing on finite amplitude distortion based second harmonic generation. Ultrason Imaging 1999;21:243–258.
Imaging parameters for tissue harmonic generation ● C.-C. SHEN et al. Liu DL, Waag RC. Correction of ultrasonic wavefront distortion using backpropagation and a reference waveform method for time-shift compensation. J Acoust Soc Am 1994;96:649 – 660. Liu DL, Waag RC. Propagation and backpropagation for ultrasonic wavefront design. IEEE Trans Ultrason Ferroelectr Freq Control 1997;44:1–12. Lu JY, Greenleaf JF. Pulse-echo imaging using a nondiffracting beam transducer. Ultrasound Med Biol 1991;17:265–281. Nowicki A, Wójcik J, Secomski W. Harmonic imaging using multitone nonlinear coding. Ultrasound Med Biol 2007;33:1112–1122. Shen CC, Li PC. Harmonic leakage and image quality degradation in tissue harmonic imaging. IEEE Trans Ultrason Ferroelectr Freq Control 2001;48:728 –736. Shen CC, Li PC. Motion artifacts of pulse inversion-based tissue harmonic imaging. IEEE Trans Ultrason Ferroelectr Freq Control 2002;49:1203–1211.
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Shen CC, Wang YC, Hsieh YC. Third harmonic transmit phasing for tissue harmonic generation. IEEE Trans Ultrason Ferroelectr Freq Control 2007;54:1370 –1381. Shung KK, Smith MB, Tsui B. Principles of Medical Imaging. New York: Academic, 1992. Simpson DH, Chin CT, Burns PN. Pulse inversion doppler: a new method for detecting nonlinear echoes from microbubble contrast agents. IEEE Trans Ultrason Ferroelectr Freq Control 1999;46: 372–382. Tranquart F, Grenier N, Eder V, Pourcelot L. Clinical use of ultrasound tissue harmonic imaging. Ultrasound Med Biol 1999;25:889 – 894. US Patent 6899679. Ultrasonic diagnosis apparatus and ultrasound imaging method; 2005. Zhou S, Hossack JA. Dynamic-transmit focusing using time-dependent focal zone and center frequency. IEEE Trans Ultrason Ferroelectr Freq Control 2003;50:142–152.
doi:10.1016/j.ultrasmedbio.2007.12.001
● Technical Note IMAGING PARAMETERS ON THIRD HARMONIC TRANSMIT PHASING FOR 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 and 3f0 signal are used to generate both frequency-sum and frequency-difference components for manipulation of tissue harmonic amplitude. Nevertheless, the acoustic propagation of 3f0 transmit signal suffers from more severe attenuation 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 transmit phasing. In this study, extensive simulations were performed to investigate the effects of these imaging parameters. Results indicate that the harmonic enhancement and suppression in 3f0 transmit phasing are compromised when the magnitude of frequency-difference component decreases in the presence of tissue attenuation and phase aberration. To compensate for the reduced frequency-difference component, a higher 3f0 transmit amplitude can be used. When the transmit parameters are concerned, a smaller 3f0 transmit aperture can provide more axially uniform harmonic enhancement and more effective suppression of harmonic amplitude. In addition, the spectral leakage signal also interferes with tissue harmonics and degrades the efficacy of 3f0 transmit phasing. Our results suggest that, in the method of 3f0 transmit phasing, the transmit amplitude, phase and aperture size of 3f0 signal should remain adjustable for optimization of clinical performance. Besides, multipulse sequences such as pulse inversion 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.
improves, especially on technically difficult bodies (Christopher 1997, 1998; Tranquart et al. 1999; Desser and Jeffrey 2001). Even with aforementioned advantages, imaging with tissue harmonic signal suffers from several difficulties. For example, under typical imaging conditions, only a small amount of harmonic signal is generated during the acoustic propagation and thus both penetration and sensitivity of tissue harmonic imaging are limited because of the lower signal-to-noise ratio (Li 1999). On the contrary, in contrast agent harmonic imaging, where microbubbles are routinely used to enhance image contrast between blood-perfused areas and tissue background, the presence of tissue harmonics may obstruct the detection of microbubble contrast agents and degrade the contrast-to-tissue ratio (CTR), especially when a higher mechanical index is adopted (Burns 1996; Chang et al. 1996; de Jong and Ten Cate 1996). Because both enhancement and suppression of tissue harmonic amplitude are essential, respectively, for tissue and contrast
INTRODUCTION Tissue harmonic signal from finite amplitude distortion of propagating sound wave is generally characterized as progressive steepening of the waveform as a result of the pressure-dependent acoustic velocity in nonlinear medium (Beyer and Letcher 1969; Haran and Cook 1983; Cain 1986). Because the tissue harmonics build up gradually with distance from the transducer, the ultrasound signal at harmonic frequency is relatively weak in the beginning of propagation. Consequently, reverberation from shallow structures such as interfaces between skin and fat can be markedly suppressed because of the low echo intensity. Besides, sidelobes of the nonlinearly generated beam are much lower than those of the linear beam and the corresponding image contrast significantly Address correspondence to: Che-Chou Shen, Department of Electrical Engineering, National Taiwan University of Science and Technology, #43, Sec.4, Keelung Rd., Taipei, 106, Taiwan. E-mail: [email protected] 1001
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imaging, there have been various techniques proposed to manipulate the tissue harmonic amplitude (Lu and Greenleaf 1991; Krishnan et al. 1998; Christopher 1999; Li and Shen 1999; Zhou and Hossack 2003; Chiao and Hao 2005). We have recently presented a novel method to change the tissue harmonic amplitude: the third harmonic (3f0) transmit phasing (Shen et al. 2007). The proposed method is based on transmitting an additional 3f0 signal together with the original fundamental signal (f0) to modify the tissue harmonic amplitude. During the nonlinear propagation in tissue, new spectral components will be generated at the sum and difference frequencies of the original transmit signals. These tissue harmonic signals are referred to as the frequency-sum component and the frequency-difference component, respectively. In conventional tissue harmonic imaging, the second harmonic signal is dominated by the frequency-sum component, which comes from the multiplication of the f0 signal with itself. Nevertheless, the frequency-difference component of second harmonic signal can also be produced from the spectral interaction between the f0 signal and the 3f0 signal when the transmit waveform consists of both signals. Note that the phase of the frequency-sum component of second harmonic signal is proportional to 2f when the fundamental transmit signal is modeled as exp(j(2f0t⫹f)). The symbol f is the phase of the f0 transmit signal. On the other hand, the frequency-difference component is related to both phases of the f0 and 3f0 transmit signals. Specifically, the phase of frequencydifference component will be provided that the 3f0 transmit signal is modeled as exp(j(2(3f0)t⫹⫹f)). The symbol represents the relative phase between the 3f0 transmit signal and the f0 transmit signal. Consequently, tissue harmonic generation can be enhanced when the two components are in-phase and being constructively summed together. Otherwise, they may cancel out each other and result in reduced tissue harmonic amplitude. In other words, the phase relation between the frequency-sum and the frequency-difference component should be ⫽ 2 f ⫹ for second harmonic suppression, whereas the relation ⫽ 2 f leads to enhancement of second harmonic amplitude. The previously mentioned two phase relations suggest that the manipulation of second harmonic amplitude can be achieved by simply tuning the 3f0 transmit phase. The 3f0 transmit phasing is very different from other approaches that simultaneously transmit two frequencies. For example, in differential tissue harmonic imaging (DTHI) from Toshiba, transmission at both f0 and 2f0 frequencies is used for additional differential harmonic signal at f0 frequency (US Patent 2005; Nowicki et al. 2007). Note that there is not spectral overlap between the
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differential harmonic signal and the second harmonic signal and, hence, the resultant harmonic amplitude does not rely on the relative phasing between transmit signals. In 3f0 transmit phasing, generation of frequencydifference component involves the 3f0 transmit signal and thus, both the axial and lateral characteristics of the frequency-difference component depend on those of the constitutive 3f0 beam. Compared with the f0 signal, the focusing of 3f0 signal is typically stronger and the acoustic power is more concentrated in the axial and lateral directions. Since the same acoustic power can be delivered to the focal zone with lower transmit amplitude at 3f0 frequency due to its stronger focusing, the amplitude of 3f0 transmit signal can be lower than the f0 transmit amplitude while the generation of frequency-sum and frequency-difference components are still approximately equal in magnitude for maximal cancellation of these two signals. For example, with the same aperture size at both f0 and 3f0 frequencies, the optimal transmit amplitude ratio of the 3f0 signal to the f0 signal is about 0.5 for harmonic suppression (Shen et al. 2007). In other words, for example, the transmit amplitude of the 3f0 signal would be about 100 kPa for maximal harmonic suppression when the corresponding f0 transmit amplitude is 200 kPa. Nevertheless, because the 3f0 transmit phasing utilizes transmission at higher frequency, its performance would vary with imaging parameters that are sensitive to frequency. In this technical note, relevant imaging parameters in 3f0 transmit phasing are investigated using simulations. This paper is organized as follows. First, the selection of relevant imaging parameters is described together with the simulation model. These imaging parameters are divided into two categories: tissue parameters and transmit parameters, and their effects are individually considered. Finally, conclusions and discussions of this study will be given. METHODS Selection of relevant imaging parameters Because the 3f0 transmit phasing relies on the frequency-difference component to achieve either constructive enhancement or destructive cancellation of the tissue harmonic signal, the beam properties of frequency-difference component would inevitably change the performance of 3f0 transmit phasing. There are several imaging parameters that could significantly change the frequencydifference component and thus result in degradation of 3f0 transmit phasing. For example, the frequency-dependent attenuation in biological tissues would markedly reduce the amplitude of 3f0 signal relative to that of the f0 signal during the acoustic propagation. Consequently, as compared with the frequency-sum component, the
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amplitude of frequency-difference component could severely decrease such that the efficacy of harmonic enhancement and suppression is limited. Another frequency-dependent tissue parameter is phase aberration. With fixed time delay error in transmit/receive channels because of tissue inhomogeneities, the corresponding phase error increases with frequency and, hence, results in more deteriorated beam at higher frequency. Consequently, the divergent 3f0 beam may also degrade the performance of 3f0 transmit phasing. In addition to those aforementioned tissue parameters, transmit parameters such as the aperture size of 3f0 transmit signal also play important roles in 3f0 transmit phasing. In enhancement mode, we have shown previously that the depth of focus of the tissue harmonic signal would become shorter because of the strong focusing of the frequency-difference component (Shen et al. 2007). Consequently, the SNR in harmonic imaging may deteriorate rapidly for off-focus region. To elongate the depth of focus in 3f0 transmit phasing, a smaller 3f0 transmit aperture can be used to generate a frequencydifference beam with longer depth of focus. The 3f0 aperture size can be readily modified in an array system by changing the number of transmit channels. Besides, when a wideband pulse is transmitted for better axial resolution, the effect of harmonic leakage cannot be ignored. The linearly propagated harmonic leakage signal has higher sidelobes than its nonlinear counterpart and thus compromises the image contrast in tissue harmonic imaging (Shen and Li 2001). The leakage signal also increases the harmonic amplitude in tissue background and hence reduces the specificity of contrast agents in harmonic imaging (Krishnan and O’Donnell 1996). Similarly, in 3f0 transmit phasing, the presence of leakage signal could also deteriorate the efficacy of tissue harmonic suppression and cause difficulties in the detection of contrast harmonic signal. Based on these observations, relevant imaging parameters including attenuation, phase aberration, 3f0 transmit aperture size and transmit signal bandwidth are considered for their effects on 3f0 transmit phasing in this study. Simulation model In the simulation model, the transmit waveform is first decomposed into discrete temporal frequency components. For each frequency component, continuous beam formation is approximated by incremental field propagation. At each increment, linear propagation is simulated based on the angular spectrum method (Goodman 1968; Liu and Waag 1997). The nonlinear propagation is modeled using the finite amplitude distortion model (Christopher 1997). As shown in the following
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equation, the finite amplitude distortion model utilizes the frequency domain solution to Burgers’ equation, i.e.
un ⫽ u⬘n ⫹ j
 f⌬z 2c2
冋兺
n⫺1
N
ku⬘ku⬘n⫺k ⫹
k⫽1
兺 nu u
⬘ ⬘ k k⫺n
k⫽n
*
册
(1)
In eqn (1), ⌬z is the propagation increment along the axial direction. The fundamental frequency is denoted by f and  is a parameter representing the nonlinearity of the propagation medium. The term u⬘n denotes the temporal velocity field at frequency nf (n is an integer) after linear propagation. Likewise, un denotes the temporal velocity field after nonlinear propagation. The sound velocity is denoted by c. A one-dimensional, 64-channel linear array is assumed to transmit the 2-MHz fundamental signal together with the corresponding 3f0 signal at 6 MHz. The array had a 0.3-mm pitch and the transmit focus was set to 55 mm away from the transducer. The propagation medium was assumed to be homogeneous unless particularly specified and the nonlinear parameter  was set to 3.5, approximating the nonlinear property of water (Law et al. 1985). For simplicity, frequency response of the transducer is ignored without loss of generality. In the simulation model, transmit signals of either continuous wave (CW) or pulse wave (PW) can be adopted. For a CW case, the harmonic signals are represented as the corresponding Fourier series of the transmit waveform. For a PW case, the simulated second harmonic signal is extracted by band-pass filtering, with a flat frequency response between 3 MHz and 5 MHz. For both CW and PW transmit, the peak acoustic pressure at fundamental frequency is 200 KPa. For the 3f0 transmit signal, its acoustic pressure is determined by the 3f0 amplitude ratio and its phase can be changed from –170° to 180°. RESULTS Effects of tissue parameters Attenuation. CW simulations were performed to study the effect of frequency-dependent attenuation on 3f0 transmit phasing. Attenuation coefficients ␣ of 0.02, 0.06 and 0.11 np/cm/MHz were considered, which correspond to the attenuation in blood, fat and liver tissues, respectively (Shung et al. 1992). The simulated second harmonic axial amplitudes, lateral beam patterns and the corresponding integrations of beam pattern are demonstrated with ␣ ⫽ 0.06 np/cm/MHz in Fig. 1d–f, respectively. For comparison, corresponding results without attenuation (i.e., ␣ ⫽ 0 np/cm/MHz) are also illustrated in Fig. 1a– c, respectively. In these simulations, the amplitude ratio of 3f0 transmit signal is fixed at 0.5. In Fig. 1a and d, the axial amplitudes of both enhancement mode
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Fig. 1. Simulated second harmonic axial amplitudes, beam patterns and integrated beam patterns with different ␣ values. Left: ␣ ⫽ 0 np/cm/MHz. Right: ␣ ⫽ 0.06 np/cm/MHz.
and suppression mode are normalized to the focal amplitude without 3f0 transmit for each ␣ value. In other words, the normalized amplitude will be larger than unity if the 3f0 transmit signal results in enhancement of harmonic amplitude. Otherwise, the suppression of harmonic generation will make the normalized amplitude less than unity. Figure 1d shows that, after attenuation, the 3f0 transmit phasing is still effective for both enhancement and suppression of second harmonic signal over a wide range of axial depths. However, it should be noted that the performance of 3f0 transmit phasing is degraded compared with that without attenuation. Specifically, the focal enhancement is reduced from about 6 dB without attenuation to only 3 dB with ␣ ⫽ 0.06 np/cm/MHz. The corresponding focal suppression is also reduced from about 11 dB without attenuation to only 6 dB with ␣ ⫽ 0.06 np/cm/MHz. In other words, when tissue attenuation is considered, 3f0 transmit phasing results in less change of second harmonic amplitude. Similar observations can be made from the beam patterns. In Fig. 1b and e, the focal beam patterns are normalized to the on-axis amplitude without 3f0 transmit for each ␣ value. Specifically, without tissue attenuation, the beam pattern of enhancement mode is more concentrated (i.e., lower sidelobes and narrower mainlobe) such that the corresponding lateral and contrast resolution are superior to that without 3f0 transmit. Nevertheless, after tissue attenuation, the radiation patterns of both enhancement and suppression modes become more similar to that without 3f0 transmit. Although the enhancement beam
still has lower sidelobes, the improvement of image quality has been compromised because of attenuation. The integrated beam patterns in Fig. 1c and f also reveal that the profiles tend to be more close to each other when the attenuation is present. The variation of second harmonic amplitude with 3f0 transmit phase at focal depth is also shown in Fig. 2. For each ␣ value, the focal second harmonic amplitudes are normalized to that without 3f0 transmit signal. It is clearly demonstrated that the extent of enhancement and suppression using 3f0 transmit phasing decreases with the attenuation. The results are as expected because a smaller amount of frequency-difference component would be generated at second harmonic frequency when its constitutive 3f0 transmit beam suffers from severe attenuation during propagation. However, it is also noticeable in Fig. 2 that the 3f0 transmit phases for maximal enhancement and suppression are insensitive to tissue attenuation. For example, the 3f0 transmit phase for maximal suppression only slightly drifts from – 60° to – 40° when the ␣ increases from 0 np/cm/MHz to 0.11 np/cm/MHz. Because the magnitude of 3f0 transmit beam is markedly reduced in the presence of attenuation and thus produces insufficient frequency-difference component, the 3f0 transmit amplitude at source should be increased to compensate the attenuated frequency-difference component. Figure 3 shows the focal second harmonic amplitudes as a function of 3f0 transmit amplitude ratio with different attenuations. It is demonstrated that the 3f0 transmit amplitude ratio for optimal suppression obviously increases with attenuation. For example, the 3f0
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Fig. 2. Simulated focal second harmonic amplitudes as a function of 3f0 transmit phase with different ␣ values. The 3f0 transmit amplitude ratio is fixed at 0.5.
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 be ignored, a higher 3f0 transmit amplitude is required to compensate the signal loss of frequency-difference component for better harmonic suppression. In addition, it should be noted that the harmonic enhancement would also benefit from the stronger 3f0 transmit signal.
Phase aberration In this study, PW simulations were performed to investigate the effect of phase aberration on 3f0 transmit phasing. In the simulations, a displaced phase screen was included to model sound velocity variations between two different media. Such a model is similar to the one proposed in Liu and Waag (1994). The medium next to the transducer had a propagation velocity of 1.45 mm/s,
Fig. 3. Simulated focal second harmonic amplitudes as a function of 3f0 transmit amplitude with different ␣ values. The 3f0 transmit phase is fixed at suppression mode.
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Fig. 4. Pattern of time delay error for 4⫻ aberration. Positive phase shift is displayed in white and the negative shift is in black.
a uniform thickness of 15 mm and a  of 6 to mimic the nonlinear properties of fat tissue (Law et al. 1985). The deeper medium is assumed to be water with a thickness of 65 mm. Time delay errors resulting from irregular thickness of fat tissue were simulated using a 2-D phase screen at the boundary of the two media. The phase screen had a correlation length of 5 mm and can be scaled to include different extent of phase error. For convenience, the phase screens with root-mean-square (RMS) time delay error of 11.6, 23.3 and 46.6 ns are referred to as 1⫻ aberration, 2⫻ aberration and 4⫻ aberration, respectively, in this paper. Gray level image of the 4⫻ aberration pattern is shown in Fig. 4. Figure 5a and c show the beam patterns at focal depth without aberration and with 4⫻ aberration, respec-
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tively. Note that the corresponding 46.6-ns RMS time delay error with the 4⫻ aberration is relatively large compared with those measured in biological tissue (Hinkelman et al. 1994, 1995) and thus significant beam distortion is expected. Compared with the case in homogeneous tissue, the beam patterns with phase aberration are markedly distorted and the resultant sidelobe levels are elevated for both enhancement and suppression. Similar observations can be made using the integrated beam patterns in Fig. 5b and d. The profile of enhancement mode converges to unity much slower compared with its no-aberration counterpart. It is also shown that, unlike the distinct difference among integration profiles without aberration, the profile of harmonic enhancement becomes similar to that without 3f0 transmit when the aberration is present. In other words, the beam quality of second harmonic signal in 3f0 transmit phasing is significantly degraded by phase aberration. The variation of focal second harmonic amplitude as a function of 3f0 transmit phase is also demonstrated using simulations in Fig. 6 with different aberrations. For each aberration, the second harmonic amplitudes with 3f0 transmit are normalized to that without 3f0 transmit. Figure 6 shows that both enhancement and suppression of second harmonic amplitude tend to be compromised when the phase error increases. It is also shown, however, that the presence of phase aberration does not result in significant change of 3f0 transmit phase for either harmonic enhancement or suppression. For example, the maximal harmonic suppression without aberration is
Fig. 5. Simulated second harmonic beam patterns and integrated beam patterns without (left) and with 4⫻ aberration (right).
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Fig. 6. Simulated focal second harmonic amplitudes as a function of 3f0 transmit phase with different aberrations. The 3f0 transmit amplitude ratio is fixed at 0.5.
achieved with a 3f0 transmit phase of 120°. When the 4⫻ aberration is included, the 3f0 transmit phase for maximal harmonic suppression slightly drifts to 140°. In other words, although the presence of phase aberration reduces the efficacy of both harmonic enhancement and suppression, the corresponding 3f0 transmit phase remains relatively unchanged. Effects of transmit parameters 3f0 transmit aperture size. In this study, the relative size of 3f0 aperture to the fundamental aperture is considered using CW simulations. In Fig. 7, the focal second harmonic amplitudes are represented as a function of both amplitude ratios and phases of 3f0 transmit signal. The 3f0 aperture sizes are 100%, 75% and 50% of the fundamental aperture size, respectively, in Fig. 7a– c. Note that, for example, the 50% 3f0 aperture uses the central 32 channels for transmit, whereas the fundamental aperture comprises the whole 64 channels. The focal second harmonic amplitudes in Fig. 7 have been normalized to that without 3f0 transmit for each 3f0 aperture and the gray bar in each panel maps the normalized harmonic amplitudes into gray levels. In Fig. 7a, it is apparent that the most effective suppression of second harmonic signal with the 100% 3f0 aperture is achieved when the 3f0 transmit amplitude ratio is scaled to about 0.45. Nevertheless, it is shown in Fig. 7b and c that the maximal harmonic suppression occurs with a higher 3f0 transmit amplitude when a smaller 3f0 aperture is used. For example, the optimal ratios for harmonic suppression change to 0.55 and 0.8,
respectively, for the 75% and 50% 3f0 apertures. The increase of 3f0 transmit amplitude ratio is as expected because a higher amplitude is necessary to maintain similar 3f0 transmit energy with a reduced aperture size. For all figures, it is also obvious that the harmonic enhancement monotonically increases with the 3f0 transmit amplitude. Moreover, the 3f0 transmit phases corresponding to harmonic enhancement and suppression do not change with different aperture sizes. For example, the 3f0 transmit phase for harmonic suppression remains at – 60° when the 3f0 aperture decreases from 100% to 50%. The second harmonic axial amplitudes and the lateral beam patterns in enhancement mode are shown in Fig. 8a and b for different 3f0 apertures. Note that, in both Fig. 8 and Fig. 9, different 3f0 transmit amplitudes are selected for different apertures based on the results in Fig. 7 to achieve maximal suppression of harmonic amplitude. When the 3f0 aperture size is reduced from 100% to 75% and 50%, the corresponding second harmonic amplitudes become more uniformly distributed in the axial direction and thus provide longer depths of focus. Nevertheless, it should be noted that the long depth of focus is achieved at the cost of image quality. As shown in Fig. 8b, for a smaller 3f0 aperture, the mainlobe becomes wider and the sidelobe levels are also elevated. Consequently, the image resolution and image contrast can be compromised because of the less directive beam. In suppression mode, the 3f0 transmit aperture also play an important role to optimize the harmonic suppression in both axial and lateral directions. As shown in Fig.
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Fig. 7. Simulated focal second harmonic amplitudes as a function of 3f0 transmit phase and 3f0 transmit amplitude ratio with different 3f0 transmit aperture sizes. From left to right: 100%, 75% and 50%, respectively.
9a, although similar harmonic suppression at focal depth can be achieved with different sizes of 3f0 apertures, the prefocal and postfocal second harmonic amplitudes become elevated with a reduced 3f0 aperture size. In the extreme case of 50% 3f0 aperture, the harmonic suppression is effective only at focal depth. Nevertheless, it is noticeable that the 75% 3f0 aperture not only provides effective harmonic suppression for a wide range of axial depths, the corresponding radiation pattern in Fig. 9b also has the lowest magnitude in the mainlobe region compared with the other two apertures. In other words, harmonic suppression with the 75% 3f0 aperture is effective over a larger range in both axial and lateral directions such that the tissue background in contrast imaging can be better suppressed. Transmit bandwidth In 3f0 transmit phasing, the presence of leakage harmonic signal would interfere with the frequency-sum and the frequency-difference components of tissue harmonic signal. PW simulations were performed to illustrate two different conditions of spectral leakage in 3f0 transmit phasing. Condition I occurs when the transmit signals at both f0 and 3f0 frequencies are wideband pulses such that the leakage signals come from both the fundamental transmit band and the 3f0 transmit band. Specifically, the transmit signal is a Gaussian pulse with a – 6 dB bandwidth of about 1.6 MHz at both f0 and 3f0
frequencies, which contains considerable spectral energy at second harmonic band. In Condition II, however, the bandwidth of the 3f0 transmit signal is reduced to about 0.6 MHz to avoid spectral leakage from the 3f0 transmit band. In other words, the f0 transmit pulse is wideband and the 3f0 transmit pulse is narrowband in Condition II. For Condition I shown in Fig. 10a– c, although the harmonic suppression mode still provides lower axial amplitudes than the enhancement mode, it should be noted that the second harmonic amplitudes are already higher than those without 3f0 transmit for all depths because of the additional leakage signal from the 3f0 transmit band. Consequently, the 3f0 transmit phasing does not provide any tissue suppression compared with the case without 3f0 transmit and, hence, no CTR improvement is expected in contrast harmonic imaging. For harmonic enhancement, the increase of harmonic amplitude is also reduced from 6 dB to about 3 dB in the presence of spectral leakage. It is also shown that the sidelobes of all beam patterns are markedly elevated because of the leakage signal such that all integration profiles converge slowly and become less distinguishable as compared with Fig. 5b, where no spectral leakage is considered. For Condition II, however, only spectral leakage from the fundamental band is present because the narrowband 3f0 transmit pulse produces negligible leakage signal. As shown in Fig. 10d, the second harmonic amplitude at source in both enhancement and suppression mode is equal to that
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Fig. 8. (a) Simulated second harmonic axial amplitudes with different 3f0 transmit aperture sizes. The 3f0 transmit phase is fixed at enhancement mode. (b) Simulated second harmonic beam patterns with different 3f0 transmit aperture sizes.
without 3f0 transmit. Accordingly, the tissue harmonic amplitude can be better suppressed as the sound wave propagates. Furthermore, when the harmonic enhancement is considered, the beam quality of tissue harmonic signal is apparently superior to that without 3f0 transmit and, hence, the corresponding integration profile in Fig. 10f rises more rapidly than others. Nevertheless, although the 3f0 transmit phasing performs better in Condition II, it should be noted that the sidelobes in enhancement beam is still much higher compared with those without leakage (i.e., in Fig. 5a) and thus the loss of contrast resolution in tissue harmonic imaging is inevitable. In addition, the presence of leakage
signal increases harmonic amplitudes, especially in the near field and, hence, the efficacy of harmonic suppression in 3f0 transmit phasing is still limited in Condition II. DISCUSSION Although this study is performed without presenting real ultrasound images, information about possible variation of image quality in 3f0 transmit phasing has been provided without loss of generality by comparing the simulated acoustic beams. In the simulations, it is assumed that the dispersion effect characterized as varia-
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Fig. 9. (a) Simulated second harmonic axial amplitudes with different 3f0 transmit aperture sizes. The 3f0 transmit phase is fixed at suppression mode. (b) Simulated second harmonic beam patterns with different 3f0 transmit aperture sizes.
tion of sound velocity with frequency is negligible. Nevertheless, the dispersion could lead to different distortion of the f0 and 3f0 beams and further degrade the method of 3f0 transmit phasing. Therefore, adequate time delay correction can be applied at the transmit part of the imaging system so as to avoid severe distortion of 3f0 transmit beam and the corresponding frequency-difference signal. Results also indicate that tissue characteristics such as frequency-dependent attenuation and tissue inhomogeneities can result in significant decrease of the magnitude of 3f0 signal during propagation. Consequently, the achievable harmonic enhancement and sup-
pression are also reduced because of the lower frequency-difference magnitude in the presence of tissue attenuation and phase aberration. To compensate for the magnitude loss of 3f0 signal during propagation, a higher transmit amplitude at 3f0 frequency can be used to generate sufficient frequency-difference component so as to cancel with the frequency-sum component for maximal harmonic suppression. The higher transmit amplitude at 3f0 frequency is also necessary in the case of a smaller 3f0 aperture. Because the 3f0 transmit phasing is sensitive to the parameters of propagation tissue, which cannot be
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Fig. 10. Simulated second harmonic axial amplitudes, beam patterns and integrated beam patterns with different conditions of spectral leakage. Left: Condition I. Right: Condition II.
known in advance, the optimal phase and amplitude of 3f0 transmit signal could vary significantly in different clinical applications. Consequently, imaging calibration is required to select these 3f0 transmit parameters. This kind of calibration can be performed automatically by measuring the tissue harmonic amplitudes with different combinations of 3f0 transmit amplitude and phase. For example, the 3f0 transmit amplitude and phase that result in the lowest tissue harmonic amplitude should be used for harmonic suppression in that particular condition. Moreover, it should be noted that the 3f0 transmit phase that corresponds to the enhancement or suppression of tissue harmonic signal is quite invariant to tissue parameters. This phenomenon 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 bandwidth at either f0 or 3f0 frequencies markedly degrades the harmonic enhancement and suppression. Nevertheless, the limitation can be avoided when the multipulse transmit scheme such as pulse inversion (PI) is adopted to remove the leakage signal (Simpson et al. 1999; Shen and Li 2002). The PI technique involves two firings with inverted waveforms for each acoustic beam line. When the returning echoes from the two firings are summed, the linearly propagated leakage signal is cancelled and only nonlinearly generated 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 the PI technique can restore the contrast resolution in tissue harmonic imaging by providing much lower sidelobes than those without PI technique. CONCLUSIONS In this paper, the performance of 3f0 transmit phasing on tissue harmonic generation is studied with various imaging parameters. It is demonstrated that the 3f0 transmit signal is susceptible to tissue parameters such as tissue attenuation and beam distortion during acoustic propagation. Consequently, in clinical applications of 3f0 transmit phasing, imaging calibration is suggested to determine the optimal phase and amplitude of the 3f0 transmit signal. It is also shown that the transmit parameters such as aperture size and bandwidth significantly change the tissue harmonic generation in 3f0 transmit phasing. Compared with using the same aperture size for both f0 and 3f0 transmit, a smaller 3f0 aperture can provide more effective harmonic suppression over a larger region in both axial and lateral directions for contrast harmonic imaging. With imaging parameters used in this study, the optimal 3f0 transmit aperture for harmonic suppression is about 75% of the f0 aperture size. When harmonic enhancement is concerned in tissue harmonic imaging, a smaller 3f0 aperture is also favorable when more uniform
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Ultrasound in Medicine and Biology
Volume 34, Number 6, 2008
Fig. 11. Simulated second harmonic beam patterns without and with the PI technique. The 3f0 transmit phase is fixed at enhancement mode.
harmonic amplitudes in the axial direction are preferred for longer depth of focus. The selection of transmit bandwidth at both f0 and 3f0 frequencies also markedly change the efficacy of 3f0 transmit phasing on harmonic enhancement and suppression. When the wideband transmit pulses are used for better axial resolution, the spectral leakage signal degrades the beam quality in tissue harmonic imaging with decreased harmonic enhancement. On the other hand, the leakage signal also reduces the achievable suppression of tissue background in contrast harmonic imaging. Therefore, removal of spectral leakage signal using multipulse transmit scheme such as PI technique is beneficial in 3f0 transmit phasing. Acknowledgments—Supported in part by the National Science Council of Taiwan under grant NSC 96-2221-E-011-143 and Intelligent Building Research Center of National Taiwan University of Science and Technology are gratefully acknowledged. We also thank the reviewers for the helpful comments.
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