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Third order harmonic imaging for biological tissues using three phase-coded pulses
Ultrasonics 44 (2006) e61–e65 www.elsevier.com/locate/ultras
Third order harmonic imaging for biological tissues using three phase-coded pulses q Qingyu Ma a
a,b
, Xiufen Gong
a,*
, Dong Zhang
a
State Key Laboratory of Modern Acoustics, Institute of Acoustics, Nanjing University, Nanjing 210093, China b Education Technique Department, Nanjing Normal University, Nanjing 210097, China Available online 30 June 2006
Abstract Compared to the fundamental and the second harmonic imaging, the third harmonic imaging shows significant improvements in image quality due to the better resolution, but it is degraded by the lower sound pressure and signal-to-noise ratio (SNR). In this study, a phase-coded pulse technique is proposed to selectively enhance the sound pressure of the third harmonic by 9.5 dB whereas the fundamental and the second harmonic components are efficiently suppressed and SNR is also increased by 4.7 dB. Based on the solution of the KZK nonlinear equation, the axial and lateral beam profiles of harmonics radiated from a planar piston transducer were theoretically simulated and experimentally examined. Finally, the third harmonic images using this technique were performed for several biological tissues and compared with the images obtained by the fundamental and the second harmonic imaging. Results demonstrate that the phase-coded pulse technique yields a dramatically cleaner and sharper contrast image. 2006 Elsevier B.V. All rights reserved. Keywords: Three phase-coded pulses; Third harmonic imaging; Biological tissues
1. Introduction It is well known that the ultrasound wave propagates nonlinearly in biological tissue and harmonic components cumulate due to the nonlinearity. Recently, much attention has been focused on the study of the nonlinear propagation [1] and the nonlinear imaging techniques [2–4]. The application of the ultrasound contrast agent (UCA) motivated the development of the nonlinear imaging in clinical diagnosis [5]. To improve the resolution and specificity of harmonic imaging, a number of multi-pulse imaging techniques [6] have been developed. Pulse inversion technique [7] is the most common used method to successfully suppress the fundamental component while enhance the second harmonic by 6 dB. Amplitude modulation technique is also proposed to achieve a cancellation of the linear component and preserve the second harmonic. The q *
This work is supported by NSFC and TWAS research grants. Corresponding author. Tel.: +86 25 83594503. E-mail address: [email protected] (X. Gong).
0041-624X/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2006.06.038
second harmonic imaging is now evident in some commercial systems [8]. Compared to the second harmonic, the third harmonic has better spatial resolution and improved beam pattern performance, but lower sound pressure. High sensitivity and wide dynamic range are needed in the receiving system to achieve an acceptable amount of SNR. Therefore, how to get the desirable third harmonic component with favorable SNR and remove the other harmonics to reduce the confusion is the key topic. In this paper, a phase-coded pulse technique is put forward to selectively enhance the third harmonic component and suppress the fundamental or the second harmonic components to acquire more useful information of tissues. Combined with the theory of the finite amplitude wave, the principle and the advantage of this technique were theoretically discussed and experimentally examined. Improvements of the axial and lateral beam profiles, the signal amplitudes and SNR for the third harmonic are demonstrated both in numerical simulations and in experiments. Compared with the fundamental and the second harmonic imaging, the processed third
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Q. Ma et al. / Ultrasonics 44 (2006) e61–e65
harmonic imaging was performed for several biological tissues and results demonstrated that the improved performance dramatically improved image clarity and contrast.
Function Generator Agilent 33250
Bracket
2. Principle and method A pulse signal with angular frequency x and initial phase u0 is radiated in medium. The wave distortion and harmonic accumulation occur during the sound propagation due to the nonlinearity. From the Bessel–Fubini series solution of the Burgers’ equation [9], the sound pressure at distance x is expressed as 1 X 2p0 J m ðmrÞ sinðmxs þ mu0 Þ; pðxÞ ¼ ð1Þ mr m¼1 where p0 is the sound pressure at the source, m is the order of the harmonics, r = x/xk is the normalized axial distance, xk = (bMk)1 is the shock formation distance, b is the nonlinearity coefficient, k = x/c0 is the wave number, M = v0/ c0 is the acoustic Mach number, v0 and c0 are the characteristic value of the velocity and isentropic sound speed, t is the transmitting time, s = t x/c0 is the retarded time. Supposing that the initial phases of the three pulse signals are u0, u0 + 2p/3 and u0 + 4p/3, the sound pressure at distance x of the nth (n = 0 to 2) pulse is pn ðxÞ ¼
1 X 2p0 J m ðmrÞ sin½mxs þ mðu0 þ 2pn=3Þ: mr m¼1
ð2Þ
Summing up the received three echo signals and substituting n = 0 to 2 into Eq. (3), the pressure amplitude of the processed mth harmonic is obtained as ( 0 J ðmrÞ sin½mðxs þ u0 Þ; m ¼ 3; 6; 9; 3 2p mr m psm ðxÞ ¼ 0; otherwise: ð3Þ Compared with the single pulse transmission mode, the processed amplitude of the third harmonic is increased by 9.5 dB, whereas the fundamental and the second harmonic components are fully suppressed.
Broadband Amplifier ENI A150 55dB
Computer
GPIB
Newport Motion Controller MM 3000 Y
GPIB Digital Oscilloscope Agilent 54810
Y X
Newport Stepper Motors Preamplifier
X
Water
Transducer Water Tank
Hydrophone Sample
Fig. 1. Schematic block diagram of the experimental system.
mitted pulses are amplified by a broadband power amplifier (ENI A150, 55 dB) and then excite the transducer. The transmission signals are received by the hydrophone and recorded by the computer through a digital oscilloscope (Agilent 54810) via GPIB interface. Processed in the computer off line, the amplitudes harmonics are obtained. 3.2. Third order harmonic enhancement The spectra of the received signals with a sample of porcine liver tissue obtained before and after the use of the phase-coded pulse technique are shown in Fig. 2, which are normalized by the maximum amplitude of the fundamental frequency. In comparison with the case of the single pulse transmission mode in Fig. 2(A), only the third as well as the sixth harmonics are evidently prominent in the processed signal in Fig. 2(B). The amplitudes of the fundamental frequency and the second harmonic are effectively suppressed by 26.5 dB and 33.3 dB, whereas the third harmonic is enhanced by 9.8 dB, which is close to the theoretical prediction of 9.5 dB. 3.3. Improvement of axial and lateral beam profiles
3. Simulation and experiments 3.1. Experimental setup The schematic block diagram of the experimental system is shown in Fig. 1. A planar transducer (diameter 8 mm, center frequency 2 MHz) and a broadband needle hydrophone (NP1000, 20 MHz) are used as transmitter and receiver. A sound permeable sample container with a thickness of 20 mm is placed between the transmitter and the hydrophone close to the hydrophone to minimize the influence of sound diffraction. A function generator (Agilent 33250A) transmits three phase-coded pulses (sine wave frequency 2 MHz, repetition frequency 1 kHz, eight cycles) with initial phases of 0, 2p/3 and 4p/3 in turn. The trans-
The nonlinear propagation of finite amplitude ultrasound beam can be simulated exactly by the Khokhlov– Zabolotskaya–Kuznetsov (KZK) nonlinear wave equation [10] and it is solved using backward implicit finite differences approximation in frequency domain [11]. The simulated axial and lateral beam profiles of the fundamental up to third harmonics at p0 = 0.5 MPa are displayed in Figs. 3 and 4. The solid lines are obtained by the numerical calculation and the dashed lines represent the experimental results. The experimental axial and lateral beam profiles coincide quite well with the corresponding theoretical simulations. By using the three phase-coded pulse technique, the energy of the processed third harmonic is three times that of the single pulse mode and it is also higher than that
Q. Ma et al. / Ultrasonics 44 (2006) e61–e65 1.1
0
A
Theoretical Experimental
1.0 0.9
-20
Normalized amplitude
Normalized magnitude (dB)
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-40
-60
Fundamental frequency
0.8
Processed third harmonic
0.7 0.6 0.5
Second harmonic
0.4 0.3
Third harmonic
0.2 0.1
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0.0
0
2
4
6
10 12 8 Frequency (MHz)
14
16
18
20
-10
-5
0
5
10
15
20
Fig. 4. Comparison of the simulated (solid) and experimental (dashed) lateral beam patterns of harmonics.
B Normalized magnitude (dB)
-15
Lateral distance (mm)
0
-20
main lobe and its 3 dB beam width is about 78% of that of the second harmonic component.
-40
4. Two-dimensional imaging for biological tissues
-60
-80 0
2
4
6
8
10
12
14
16
18
20
Frequency (MHz)
Fig. 2. Spectra of the received signal (A) and the processed signal (B).
1.1
Theoretical Experimental
1.0 0.9 0.8
Normalized amplitude
-20
0.7
Fundamental frequency 0.6 0.5
Processed third harmonic
0.4
Second harmonic
0.3
In this paper, the third harmonic imaging using three phase-coded pulses was performed for several animal biological tissues in vitro. In the mechanical scanning, the sample container is mounted on the New Port stepper motors (resolution 1 lm) and scanned along x and y directions in a 20 mm · 20 mm area with a step of 0.4 mm. At each point, three pulses with initial phases of 0, 2p/3 and 4p/3 were transmitted in turn. The corresponding echo signals were acquired by the digital oscilloscope. By means of signal summation and FFT spectrum analysis, the amplitudes of harmonic components were achieved. Thus the 50 · 50 sample pixel images of the processed third harmonic were reconstructed. For comparison, the images at the fundamental and the second harmonic components of the single pulse mode were also provided. Fig. 5 displays two structural sketch maps of the biological tissue models. Model (A) is a piece of porcine fatty tissue with anomalous quadrangular liver tissue in the middle. Model (B) is a three-layer model with the porcine fatty tissue placed in the external and liver tissue located in the center with a 1 mm diameter hole.
0.2 0.1
Third harmonic
0.0 0
10
20
30
40
50
60
70
Fatty tissue
Axial distance (mm)
Fig. 3. Comparison of the simulated (solid) and experimental (dashed) axial beam profiles of harmonics.
Liver tissue
Water
of the second harmonic at distance x > 28 mm. The third harmonic has the least side lobe level and the narrowest
model (A)
model (B)
Fig. 5. Structural sketch maps of biological tissue models.
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Q. Ma et al. / Ultrasonics 44 (2006) e61–e65
Fig. 6. Reconstructed images of tissue sample (A): (a) the fundamental image, (b) the second harmonic image and (c) the processed third harmonic image.
Fig. 7. Reconstructed images of tissue sample (B): (a) the fundamental image, (b) the second harmonic image and (c) the processed third harmonic image.
The reconstructed images for the models are displayed in Figs. 6 and 7 and the images coincide well with the corresponding structural sketch maps. The dimensions of the liver tissues of the fundamental image in Figs. 6(a) and 7(a) are different from the actual size and the boundary is vague with broad intergradations. The shape of the liver tissue in Fig. 6(a) is distorted and the little hole in Fig. 7(a) is disappeared. The lower brightness in Figs. 6(b) and 7(b) is observed for the lower energy of the second harmonic. By means of the phase-coded pulse technique, better contrast performance between the different tissues is found. The dimensions of liver and fatty tissues are accurately confirmed, the tissue edges are clearly displayed and the speckle noise was also effectively reduced in Figs. 6(c) and 7(c). Therefore, considerable improvements in image quality are brought about. 5. Conclusion Based on the nonlinear propagation of the finite amplitude wave theory, the principle and the advantage of this technique are theoretically discussed and experimentally examined by the measurements of the axial and lateral beam profiles. Both the simulated and the measured results demonstrate that this technique could efficiently enhance the third harmonic by 9.7 dB and suppress the fundamental and the second harmonic perfectly to degrade the confu-
sion in harmonic imaging. Compared with the fundamental and the second harmonic images, the third harmonic images using the phase-coded pulse technique is carried out for several biological tissues and results proved that this technique can dramatically improve the image quality in contrast and resolution performance. References [1] X.F. Gong, Z.M. Zhu, T. Shi, J.H. Huang, Determination of acoustic nonlinearity parameter in biological media using FAIS and ITD methods, J. Acoust. Soc. Am. 86 (1989) 1. [2] X.F. Gong, D. Zhang, J.H. Liu, H.L. Wang, Y.S. Yan, X.C. Xu, Study of acoustic no linearity parameter imaging in reflection mode for biological tissues, J. Acoust. Soc. Am. 116 (2004) 1819. [3] F. Tranquart, N. Grenier, V. Eder, L. Pourcelot, Clinical use of ultrasound tissue harmonic imaging, Ultrasound Med. Biol. 6 (1999) 889. [4] D. Zhang, X.F. Gong, Experimental investigation of acoustic nonlinearity parameter tomography for excised pathological biological tissues, Ultrasound Med. Biol. 25 (1999) 593. [5] N. de Jong, A. Bouakaz, F.J.T. Cate, Contrast harmonic imaging, Ultrasonics 40 (2002) 567. [6] W. Wilkenning, M. Krueger, H., Ermert, Phase-coded pulse sequence for non-linear imaging, in: IEEE Ultrasonics Symposium, 2000, p. 1559. [7] C.C. Shen, P.C. Li, Motion artifacts of phase inversion-based tissue harmonic imaging, IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 9 (2002) 1203. [8] F. Tranquart, N. Grenier, V. Eder, L. Pourcelot, Clinical use of ultrasound tissue harmonic imaging, Ultrasound Med. Biol. 6 (1999) 889.
Q. Ma et al. / Ultrasonics 44 (2006) e61–e65 [9] R.T. Beyer, Nonlinear acoustics, Naval Ship System Command, Dept. of the Navy, Washington, DC, 1974, p. 91. [10] V. Kuznetsov, Equation of nonlinear acoustics, Sov. Phys. Acoust. 16 (1970) 467.
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[11] V.A. Khokhlova, R. Souchon, J. Tavakkoli, O.A. Sapozhnikov, D. Cathignol, Numerical modeling of finite-amplitude sound beams: shock formation in the near field of a cw plane piston source, J. Acoust. Soc. Am. 110 (2001) 95.
Third order harmonic imaging for biological tissues using three phase-coded pulses q Qingyu Ma a
a,b
, Xiufen Gong
a,*
, Dong Zhang
a
State Key Laboratory of Modern Acoustics, Institute of Acoustics, Nanjing University, Nanjing 210093, China b Education Technique Department, Nanjing Normal University, Nanjing 210097, China Available online 30 June 2006
Abstract Compared to the fundamental and the second harmonic imaging, the third harmonic imaging shows significant improvements in image quality due to the better resolution, but it is degraded by the lower sound pressure and signal-to-noise ratio (SNR). In this study, a phase-coded pulse technique is proposed to selectively enhance the sound pressure of the third harmonic by 9.5 dB whereas the fundamental and the second harmonic components are efficiently suppressed and SNR is also increased by 4.7 dB. Based on the solution of the KZK nonlinear equation, the axial and lateral beam profiles of harmonics radiated from a planar piston transducer were theoretically simulated and experimentally examined. Finally, the third harmonic images using this technique were performed for several biological tissues and compared with the images obtained by the fundamental and the second harmonic imaging. Results demonstrate that the phase-coded pulse technique yields a dramatically cleaner and sharper contrast image. 2006 Elsevier B.V. All rights reserved. Keywords: Three phase-coded pulses; Third harmonic imaging; Biological tissues
1. Introduction It is well known that the ultrasound wave propagates nonlinearly in biological tissue and harmonic components cumulate due to the nonlinearity. Recently, much attention has been focused on the study of the nonlinear propagation [1] and the nonlinear imaging techniques [2–4]. The application of the ultrasound contrast agent (UCA) motivated the development of the nonlinear imaging in clinical diagnosis [5]. To improve the resolution and specificity of harmonic imaging, a number of multi-pulse imaging techniques [6] have been developed. Pulse inversion technique [7] is the most common used method to successfully suppress the fundamental component while enhance the second harmonic by 6 dB. Amplitude modulation technique is also proposed to achieve a cancellation of the linear component and preserve the second harmonic. The q *
This work is supported by NSFC and TWAS research grants. Corresponding author. Tel.: +86 25 83594503. E-mail address: [email protected] (X. Gong).
0041-624X/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2006.06.038
second harmonic imaging is now evident in some commercial systems [8]. Compared to the second harmonic, the third harmonic has better spatial resolution and improved beam pattern performance, but lower sound pressure. High sensitivity and wide dynamic range are needed in the receiving system to achieve an acceptable amount of SNR. Therefore, how to get the desirable third harmonic component with favorable SNR and remove the other harmonics to reduce the confusion is the key topic. In this paper, a phase-coded pulse technique is put forward to selectively enhance the third harmonic component and suppress the fundamental or the second harmonic components to acquire more useful information of tissues. Combined with the theory of the finite amplitude wave, the principle and the advantage of this technique were theoretically discussed and experimentally examined. Improvements of the axial and lateral beam profiles, the signal amplitudes and SNR for the third harmonic are demonstrated both in numerical simulations and in experiments. Compared with the fundamental and the second harmonic imaging, the processed third
e62
Q. Ma et al. / Ultrasonics 44 (2006) e61–e65
harmonic imaging was performed for several biological tissues and results demonstrated that the improved performance dramatically improved image clarity and contrast.
Function Generator Agilent 33250
Bracket
2. Principle and method A pulse signal with angular frequency x and initial phase u0 is radiated in medium. The wave distortion and harmonic accumulation occur during the sound propagation due to the nonlinearity. From the Bessel–Fubini series solution of the Burgers’ equation [9], the sound pressure at distance x is expressed as 1 X 2p0 J m ðmrÞ sinðmxs þ mu0 Þ; pðxÞ ¼ ð1Þ mr m¼1 where p0 is the sound pressure at the source, m is the order of the harmonics, r = x/xk is the normalized axial distance, xk = (bMk)1 is the shock formation distance, b is the nonlinearity coefficient, k = x/c0 is the wave number, M = v0/ c0 is the acoustic Mach number, v0 and c0 are the characteristic value of the velocity and isentropic sound speed, t is the transmitting time, s = t x/c0 is the retarded time. Supposing that the initial phases of the three pulse signals are u0, u0 + 2p/3 and u0 + 4p/3, the sound pressure at distance x of the nth (n = 0 to 2) pulse is pn ðxÞ ¼
1 X 2p0 J m ðmrÞ sin½mxs þ mðu0 þ 2pn=3Þ: mr m¼1
ð2Þ
Summing up the received three echo signals and substituting n = 0 to 2 into Eq. (3), the pressure amplitude of the processed mth harmonic is obtained as ( 0 J ðmrÞ sin½mðxs þ u0 Þ; m ¼ 3; 6; 9; 3 2p mr m psm ðxÞ ¼ 0; otherwise: ð3Þ Compared with the single pulse transmission mode, the processed amplitude of the third harmonic is increased by 9.5 dB, whereas the fundamental and the second harmonic components are fully suppressed.
Broadband Amplifier ENI A150 55dB
Computer
GPIB
Newport Motion Controller MM 3000 Y
GPIB Digital Oscilloscope Agilent 54810
Y X
Newport Stepper Motors Preamplifier
X
Water
Transducer Water Tank
Hydrophone Sample
Fig. 1. Schematic block diagram of the experimental system.
mitted pulses are amplified by a broadband power amplifier (ENI A150, 55 dB) and then excite the transducer. The transmission signals are received by the hydrophone and recorded by the computer through a digital oscilloscope (Agilent 54810) via GPIB interface. Processed in the computer off line, the amplitudes harmonics are obtained. 3.2. Third order harmonic enhancement The spectra of the received signals with a sample of porcine liver tissue obtained before and after the use of the phase-coded pulse technique are shown in Fig. 2, which are normalized by the maximum amplitude of the fundamental frequency. In comparison with the case of the single pulse transmission mode in Fig. 2(A), only the third as well as the sixth harmonics are evidently prominent in the processed signal in Fig. 2(B). The amplitudes of the fundamental frequency and the second harmonic are effectively suppressed by 26.5 dB and 33.3 dB, whereas the third harmonic is enhanced by 9.8 dB, which is close to the theoretical prediction of 9.5 dB. 3.3. Improvement of axial and lateral beam profiles
3. Simulation and experiments 3.1. Experimental setup The schematic block diagram of the experimental system is shown in Fig. 1. A planar transducer (diameter 8 mm, center frequency 2 MHz) and a broadband needle hydrophone (NP1000, 20 MHz) are used as transmitter and receiver. A sound permeable sample container with a thickness of 20 mm is placed between the transmitter and the hydrophone close to the hydrophone to minimize the influence of sound diffraction. A function generator (Agilent 33250A) transmits three phase-coded pulses (sine wave frequency 2 MHz, repetition frequency 1 kHz, eight cycles) with initial phases of 0, 2p/3 and 4p/3 in turn. The trans-
The nonlinear propagation of finite amplitude ultrasound beam can be simulated exactly by the Khokhlov– Zabolotskaya–Kuznetsov (KZK) nonlinear wave equation [10] and it is solved using backward implicit finite differences approximation in frequency domain [11]. The simulated axial and lateral beam profiles of the fundamental up to third harmonics at p0 = 0.5 MPa are displayed in Figs. 3 and 4. The solid lines are obtained by the numerical calculation and the dashed lines represent the experimental results. The experimental axial and lateral beam profiles coincide quite well with the corresponding theoretical simulations. By using the three phase-coded pulse technique, the energy of the processed third harmonic is three times that of the single pulse mode and it is also higher than that
Q. Ma et al. / Ultrasonics 44 (2006) e61–e65 1.1
0
A
Theoretical Experimental
1.0 0.9
-20
Normalized amplitude
Normalized magnitude (dB)
e63
-40
-60
Fundamental frequency
0.8
Processed third harmonic
0.7 0.6 0.5
Second harmonic
0.4 0.3
Third harmonic
0.2 0.1
-80
0.0
0
2
4
6
10 12 8 Frequency (MHz)
14
16
18
20
-10
-5
0
5
10
15
20
Fig. 4. Comparison of the simulated (solid) and experimental (dashed) lateral beam patterns of harmonics.
B Normalized magnitude (dB)
-15
Lateral distance (mm)
0
-20
main lobe and its 3 dB beam width is about 78% of that of the second harmonic component.
-40
4. Two-dimensional imaging for biological tissues
-60
-80 0
2
4
6
8
10
12
14
16
18
20
Frequency (MHz)
Fig. 2. Spectra of the received signal (A) and the processed signal (B).
1.1
Theoretical Experimental
1.0 0.9 0.8
Normalized amplitude
-20
0.7
Fundamental frequency 0.6 0.5
Processed third harmonic
0.4
Second harmonic
0.3
In this paper, the third harmonic imaging using three phase-coded pulses was performed for several animal biological tissues in vitro. In the mechanical scanning, the sample container is mounted on the New Port stepper motors (resolution 1 lm) and scanned along x and y directions in a 20 mm · 20 mm area with a step of 0.4 mm. At each point, three pulses with initial phases of 0, 2p/3 and 4p/3 were transmitted in turn. The corresponding echo signals were acquired by the digital oscilloscope. By means of signal summation and FFT spectrum analysis, the amplitudes of harmonic components were achieved. Thus the 50 · 50 sample pixel images of the processed third harmonic were reconstructed. For comparison, the images at the fundamental and the second harmonic components of the single pulse mode were also provided. Fig. 5 displays two structural sketch maps of the biological tissue models. Model (A) is a piece of porcine fatty tissue with anomalous quadrangular liver tissue in the middle. Model (B) is a three-layer model with the porcine fatty tissue placed in the external and liver tissue located in the center with a 1 mm diameter hole.
0.2 0.1
Third harmonic
0.0 0
10
20
30
40
50
60
70
Fatty tissue
Axial distance (mm)
Fig. 3. Comparison of the simulated (solid) and experimental (dashed) axial beam profiles of harmonics.
Liver tissue
Water
of the second harmonic at distance x > 28 mm. The third harmonic has the least side lobe level and the narrowest
model (A)
model (B)
Fig. 5. Structural sketch maps of biological tissue models.
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Q. Ma et al. / Ultrasonics 44 (2006) e61–e65
Fig. 6. Reconstructed images of tissue sample (A): (a) the fundamental image, (b) the second harmonic image and (c) the processed third harmonic image.
Fig. 7. Reconstructed images of tissue sample (B): (a) the fundamental image, (b) the second harmonic image and (c) the processed third harmonic image.
The reconstructed images for the models are displayed in Figs. 6 and 7 and the images coincide well with the corresponding structural sketch maps. The dimensions of the liver tissues of the fundamental image in Figs. 6(a) and 7(a) are different from the actual size and the boundary is vague with broad intergradations. The shape of the liver tissue in Fig. 6(a) is distorted and the little hole in Fig. 7(a) is disappeared. The lower brightness in Figs. 6(b) and 7(b) is observed for the lower energy of the second harmonic. By means of the phase-coded pulse technique, better contrast performance between the different tissues is found. The dimensions of liver and fatty tissues are accurately confirmed, the tissue edges are clearly displayed and the speckle noise was also effectively reduced in Figs. 6(c) and 7(c). Therefore, considerable improvements in image quality are brought about. 5. Conclusion Based on the nonlinear propagation of the finite amplitude wave theory, the principle and the advantage of this technique are theoretically discussed and experimentally examined by the measurements of the axial and lateral beam profiles. Both the simulated and the measured results demonstrate that this technique could efficiently enhance the third harmonic by 9.7 dB and suppress the fundamental and the second harmonic perfectly to degrade the confu-
sion in harmonic imaging. Compared with the fundamental and the second harmonic images, the third harmonic images using the phase-coded pulse technique is carried out for several biological tissues and results proved that this technique can dramatically improve the image quality in contrast and resolution performance. References [1] X.F. Gong, Z.M. Zhu, T. Shi, J.H. Huang, Determination of acoustic nonlinearity parameter in biological media using FAIS and ITD methods, J. Acoust. Soc. Am. 86 (1989) 1. [2] X.F. Gong, D. Zhang, J.H. Liu, H.L. Wang, Y.S. Yan, X.C. Xu, Study of acoustic no linearity parameter imaging in reflection mode for biological tissues, J. Acoust. Soc. Am. 116 (2004) 1819. [3] F. Tranquart, N. Grenier, V. Eder, L. Pourcelot, Clinical use of ultrasound tissue harmonic imaging, Ultrasound Med. Biol. 6 (1999) 889. [4] D. Zhang, X.F. Gong, Experimental investigation of acoustic nonlinearity parameter tomography for excised pathological biological tissues, Ultrasound Med. Biol. 25 (1999) 593. [5] N. de Jong, A. Bouakaz, F.J.T. Cate, Contrast harmonic imaging, Ultrasonics 40 (2002) 567. [6] W. Wilkenning, M. Krueger, H., Ermert, Phase-coded pulse sequence for non-linear imaging, in: IEEE Ultrasonics Symposium, 2000, p. 1559. [7] C.C. Shen, P.C. Li, Motion artifacts of phase inversion-based tissue harmonic imaging, IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 9 (2002) 1203. [8] F. Tranquart, N. Grenier, V. Eder, L. Pourcelot, Clinical use of ultrasound tissue harmonic imaging, Ultrasound Med. Biol. 6 (1999) 889.
Q. Ma et al. / Ultrasonics 44 (2006) e61–e65 [9] R.T. Beyer, Nonlinear acoustics, Naval Ship System Command, Dept. of the Navy, Washington, DC, 1974, p. 91. [10] V. Kuznetsov, Equation of nonlinear acoustics, Sov. Phys. Acoust. 16 (1970) 467.
e65
[11] V.A. Khokhlova, R. Souchon, J. Tavakkoli, O.A. Sapozhnikov, D. Cathignol, Numerical modeling of finite-amplitude sound beams: shock formation in the near field of a cw plane piston source, J. Acoust. Soc. Am. 110 (2001) 95.