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Intravascular ultrasound tissue harmonic imaging: A simulation study
Ultrasonics 44 (2006) e185–e188 www.elsevier.com/locate/ultras
Intravascular ultrasound tissue harmonic imaging: A simulation study M.E. Frijlink a
a,*
, D.E. Goertz
a,b
, A. Bouakaz c, A.F.W. van der Steen
a,b
Biomedical Engineering, Erasmus MC, University Medical Center Rotterdam, The Netherlands b Interuniversity Cardiology Institute of the Netherlands, Utrecht, The Netherlands c Universite´ F. Rabelais, Tours, France Available online 30 June 2006
Abstract Recently, the in vivo feasibility of tissue harmonic imaging (THI) with a mechanically-rotated intravascular ultrasound (IVUS) catheter was experimentally demonstrated. To isolate the second harmonic signal content, both pulse inversion (PI) and analog filtering were used. In the present paper, we report the development of a simulation tool to investigate nonlinear IVUS beams and the influence of rotation on the efficiency of PI signal processing. Nonlinear 20 MHz beams were simulated in a homogeneous tissue-mimicking medium, resulting in second harmonic pressure fields at 40 MHz. The acoustic response from tissue was simulated by summing radio-frequency (RF) pulse–echo responses from many point-scatterers. When the transducer was rotated with respect to the point-scatterers, the fundamental frequency suppression using PI degraded rapidly with increasing inter-pulse angles. The results of this study will aid in the optimization of harmonic IVUS imaging systems. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Intravascular ultrasound; Nonlinear; Tissue harmonic imaging; Simulation
1. Introduction Intravascular ultrasound (IVUS) is capable of providing real time cross-sectional images of coronary arteries and, therefore, it has become an important clinical tool for the detection and evaluation of coronary artery diseases as well as for therapy guidance and clinical research [1]. At present, clinicians generally use rotating single-element IVUS catheters with center frequencies between 30 and 40 MHz. Tissue harmonic imaging (THI) has been shown to increase the diagnostic value of conventional echocardiography below 10 MHz by improving the image quality. We previously developed an experimental set-up to study the feasibility and potential of THI at IVUS frequencies. The suppression of stent imaging artifacts was shown when high frequency THI (transmit fc = 20 MHz, receive fc = 40 MHz) was applied in vitro [2]. More recently, we * Corresponding author. Present address: Thorax Center Ee23.02, Erasmus MC, PO Box 1738, 3000 DR Rotterdam, The Netherlands. Tel.: +31 10 4088031; fax: +31 10 4089445. E-mail address: [email protected] (M.E. Frijlink).
0041-624X/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2006.06.044
demonstrated in vivo the feasibility of THI for an IVUS system using a 20–40 MHz mechanically-rotated IVUS catheter [3]. In that study, tissue harmonic signals were isolated using a combination of analog filtering and pulseinversion (PI). The PI technique requires (at least) two firings of a pulse and its inverted counterpart for each acoustic line [4]. With tissue or catheter motion, the fundamental frequency signal (i.e., transmit bandwidth signal) is not completely cancelled, and the harmonic intensity becomes smaller due to signal misalignment. Motion artifacts of PI-based THI have been studied by Shen and Li [5]. Their results indicated that the tissue harmonic signal is significantly affected by tissue motion, and that for axial motion, the tissue harmonic intensity decreases much more rapidly than with lateral motion. This study was conducted under conditions relevant to low frequency array based scanning. A number of different approaches have been developed to model the nonlinear propagation in the field of an ultrasonic transducer [6]. The most common approach is to solve the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation, which is a nonlinear parabolic equation that
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M.E. Frijlink et al. / Ultrasonics 44 (2006) e185–e188
accounts for the combined effects of diffraction, absorption, and nonlinearity for directional sound beams [7]. Comparisons of nonlinear simulation results and measurements show excellent agreement [6],[8]. For relatively short pulses, as typically used in diagnostic ultrasound, the timedomain implementation of the KZK-equation is advantageous because many harmonic components could then be taken into account for the relatively broadband imaging pulses [7]. In this study, we simulated fundamental 20 MHz (F20), second harmonic (H40), and fundamental 40 MHz (F40) fields for an unfocused circular IVUS element using a two dimensional nonlinear parabolic KZK-equation and medium characteristics (attenuation, nonlinearity, scattering) in the range of those of vascular tissue and blood. The pulse–echo responses from point-scatterers, randomly positioned in three dimensions, were calculated for successive inverted pulses as the beam was rotated. The influence of rotation on the performance of PI was then investigated. 2. Methods 2.1. Simulation design The simulation of the transmitted nonlinear field by an unfocused circular transducer is based on a time-domain implementation of the KZK-equation based on Lee and Hamilton’s numerical approach [9]. The two dimensional implementation has been written in FORTRAN and has been previously evaluated [10]. The attenuation of acoustic waves propagating in a wide variety of lossy media obeys a power law dependence on frequency. The algorithm described by Bouakaz et al. [10] was modified to account for a frequency dependent attenuation different than a power law exponent of 2 (which corresponds to the power law exponent of attenuation of water). The received signal from an individual scatterer is calculated using an analytically derived spatial impulse response for an unfocused circular transducer [11]. In order to be able to use this spatial impulse response in combination with propagation in a frequency dependent attenuating medium, the distance from an individual point-scatterer to the piston transducer is approximated by a single value, similar to the approach described by Jensen et al. [12]. For the purpose of simulating ultrasound backscattered signals, tissue can be represented by many point scatterers positioned randomly in three dimensions [13],[14]. All point scatterers were assigned the same scattering strength and frequency dependent backscatter was taken into account. The backscatter signal from the cloud of scatterers is calculated by a summation of the individual responses from each scatterer. The scatterer density was sufficient to produce Rayleigh envelope statistics. The three-dimensional scatterer volume could be rotated with respect to the transmitted field to simulate catheter rotation of a mechanically scanned IVUS transducer.
2.2. Simulation parameters The nonlinear beams were calculated for a circular, unfocused transducer with a diameter of 0.9 mm, similar to IVUS elements used in previous IVUS THI studies [3]. Due to the circular symmetry, a two-dimensional simulation is sufficient to calculate three-dimensional fields. In all calculations, the excitation pulse was a Gaussian enveloped sine wave with a 30% fractional bandwidth. The propagation medium characteristics were chosen to be in the range of those of vascular tissue and blood. Arterial tissue and blood have a frequency dependent attenuation with power law exponents of 1.1 and 1.2, respectively, in the frequency range from 15 to 60 MHz [15],[16]. In the 10–50 MHz range, this is approximated by an attenuation that has a linear frequency dependency in the range from 0.5 to 1.5 dB/cm/MHz. In this study, a frequency dependent attenuation value of 1.0 dB/cm/MHz was used. The sound speed of the propagation medium was chosen to be 1560 m/s, the mass density 1050 kg/m3 and the nonlinear parameter (B/A) 6.0 [17]. The backscatter signal from the scatterers is calculated by the summation of responses from all scatterers that are within the 20 dB beamwidth. In our case, this means that all scatterers within a distance of 0.5 mm from the zaxis (corresponding to the propagation axis) are taken into account between z = 0.5 and z = 6.0 mm. Lockwood et al. [15] showed that the power law exponent of the frequency dependent backscatter in the artery wall ranged between c = 1.1 and 1.4, and that this parameter of blood ranged from c = 1.3 to 1.4 in the same frequency range. A frequency dependence of c = 1.3 has been chosen in this study. 2.3. Simulations 2.3.1. Nonlinear beam simulations Two-dimensional beam profiles were calculated in F20 and H40 mode for a maximum fundamental excitation pressure of 2 MPa. For comparison, a F40 beam profile was also calculated at a low excitation pressure of 50 kPa. 2.3.2. Effects of rotation on pulse inversion To study the effect of catheter rotation on the effectiveness of PI in suppressing fundamental frequency energy, two inverted 20 MHz pulses (0° and 180°) were propagated through the attenuating medium. Echoes from multiple point-scatterers have been calculated to simulate the RF pulse–echo responses at different angles with respect to the IVUS transducer. Fig. 1 shows the simulation set-up, showing the circular transducer and the point-scatterers. One data set consisting of 32 different realizations of a volume of randomly positioned scatterers was calculated for a F20 2 MPa amplitude pulse-pair. The average cross-correlation value between RF-lines was calculated as a function
M.E. Frijlink et al. / Ultrasonics 44 (2006) e185–e188
e187
Average cross-correlation between RF-lines [2-3 mm] raw RF H40 RF F40 RF
Cross-correlation
1 0.8 0.6 0.4 0.2 0 -0.2
α
Fig. 1. Schematic simulation set-up, showing randomly distributed pointscatterers in a 3D volume with respect to a rotating transducer.
of inter-pulse angle. This is done for both raw and filtered RF-lines (32–50 MHz, 5th order Butterworth). For comparison, the average cross-correlation for F40 RF-lines has also been calculated. The incremental inter-pulse angle was 0.15°, which corresponded to the experimentally employed line-density of 2400 RF-lines per rotation [3]. The effectiveness of PI for fundamental frequency suppression was studied at a distance of 2–3 mm from the transducer as a function of inter-pulse angle. The mean fundamental signal content of pulse-pairs was calculated by summing the frequency content between 18 and 22 MHz. 3. Results 3.1. Nonlinear beam simulations Two-dimensional beam profiles for F20, H40 and F40 modes are plotted in Fig. 2. These images are normalized
-4
-2 0 2 4 Inter-pulse angle [degrees]
6
Fig. 3. Cross-correlation between raw, H40 and F40 RF-lines at a distance from 2 to 3 mm from the transducer, plotted as a function of inter-pulse angle (in degrees).
with respect to the maximum signal within the individual images. The H40 beam shows less near field energy and a reduction in sidelobe energy compared to both F20 and F40. The attenuation of the medium causes the F40 to decay faster than both F20 and H40. 3.2. Effects of rotation on pulse inversion The average inter-pulse cross-correlation estimates for the raw, H40 and F40 RF-lines is given in Fig. 3 as a function of inter-pulse angle. These curves show the mean of 100 cross-correlation curves for windowed RF-lines corresponding to backscatter from 2 to 3 mm from the transducer. It can be seen that the cross-correlation peak is narrower for H40 and narrowest for F40, which is attributed to the beam width at this distance (Fig. 2). These curves indicate the legitimacy of averaging neighboring RF-lines to improve the signal-to-noise ratio (SNR) for small inter-pulse angles. For example, the decorrelation between H40 RF-lines (from 2 to 3 mm) is only <0.1 within an angle of 0.5°. The fundamental suppression through PI at a distance of 2–3 mm for the 2 MPa amplitude pulse-pair (0° and
Fig. 2. Two-dimensional beamprofiles in F20, H40 and F40 mode. The beamprofiles have been normalized with respect to the maximum signal within individual images.
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Average fundamental reduction Fundamental suppression [dB]
30 25 20 15 10 5 0 0
2
4 6 8 Inter-pulse angle [degrees]
10
Fig. 4. The fundamental suppression with PI as a function of inter-pulse angle as calculated for a 2 MPa pulse-pair calculated for backscatter 2–3 mm from the transducer.
180°) is expressed as a function of inter-pulse angle in Fig. 4. This figure shows that the fundamental suppression decreases rapidly with increasing inter-pulse angles, which is linked to the reduced cross-correlation between raw F20 RF-lines for increasing inter-pulse angles (Fig. 3). Thus, a reduced line-density corresponding to an increased inter-pulse angle, leads to a reduced fundamental suppression when PI is applied. Fig. 4 indicates a fundamental suppression of 16 and 10 dB when PI is applied with an interpulse angle of 0.70° and 1.4°, respectively, corresponding to approximately 512 and 256 RF-lines per rotation. These line-densities correspond to those used in current clinical mechanically scanned IVUS systems. 4. Conclusion and discussion Nonlinear fields at 20–40 MHz have been simulated for circular IVUS transducers through media with frequency dependent attenuation values in the range of those of vascular tissue and blood. The influence of transducer rotation on the fundamental suppression of pulse inversion has been studied for a range of inter-pulse angles. In the simulations with a rotating transducer, the minimal inter-pulse angle was chosen to be 0.15°, based on a line-density of 2400 lines per rotation. Using this line-density, the commercially and clinically used rotational speed of thirty rotations per second will than result in a pulse-repetition-frequency (PRF) of approximately 75 kHz, which is still lower than the maximum PRF of a rotating single-element IVUS system as limited by sound propagation speed. So in spite of a lower line-density (e.g., 256 lines per rotation) at 30 rotations per second of current commercially available IVUS systems, no physical limitations exist to increase to a line-density of 2400 lines per rotation. A degradation of fundamental suppression with PI was observed for increasing inter-pulse angles. This is due to increased decorrelation between RF pulse-pairs for increas-
ing inter-pulse angles. Future simulations might gain insight in the competing effects of decorrelation and pulse averaging, resulting in a trade-off between SNR and resolution. The results from this simulation study will guide the optimization of harmonic IVUS systems with mechanically scanned single-element catheters. The PRF, line-density and transducer size and geometry could be altered to optimize the fundamental suppression with PI. This simulation tool could also be used to investigate different pulse schemes (coded excitation) for isolating harmonic signals. Further, such simulations may also be useful in the context of guiding the implementation and optimization of nonlinear contrast imaging systems. References [1] Y. Saijo, A.F.W. van der Steen, Vascular Ultrasound, SpringerVerlag, Tokyo, 2003. [2] M.E. Frijlink, D.E. Goertz, A.F.W. van der Steen, Reduction of stent artifacts using high-frequency harmonic ultrasound imaging, Ultrasound in Medicine and Biology 31 (2005) 1335. [3] M.E. Frijlink, D.E. Goertz, L.C.A. van Damme, R. Krams, A.F.W. van der Steen, Intravascular ultrasound tissue harmonic imaging in vivo, IEEE Ultrasonics Symposium (2004) 1118. [4] D.H. Simpson, C.T. Chin, P.N. Burns, Pulse inversion doppler: A new method for detecting nonlinear echoes from microbubble contrast agents, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 46 (1999) 372. [5] C.C. Shen, P.C. Li, Motion artifacts of pulse inversion-based tissue harmonic imaging, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 49 (2002) 1203. [6] V.F. Humphrey, Nonlinear propagation in ultrasonic fields: Measurements, modelling and harmonic imaging, Ultrasonics 38 (2000) 267. [7] M.F. Hamilton, D.T. Blackstock, Nonlinear Acoustics, Academic Press, San Diego, 1998. [8] F.A. Duck, Nonlinear acoustics in diagnostic ultrasound, Ultrasound in Medicine and Biology 28 (2002) 1. [9] Y.S. Lee, M.F. Hamilton, Time-domain modeling of pulsed finiteamplitude sound beams, Journal of the Acoustical Society of America 97 (1995) 906. [10] A. Bouakaz, C.T. Lancee, N. de Jong, Harmonic ultrasonic field of medical phased arrays: Simulations and measurements, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 50 (2003) 730. [11] P.R. Stephanishen, Transient radiation from pistons in an infinite planar baffle, Journal of the Acoustical Society of America 49 (1971) 1629. [12] J.A. Jensen, D. Gandhi, W.D. O’Brien, Ultrasound fields in an attenuating medium, IEEE Ultrasonics Symposium (1993) 943. [13] A.T. Kerr, J.W. Hunt, A method for computer simulation of ultrasound doppler color flow images-i. Theory and numerical method, Ultrasound in Medicine and Biology 18 (1992) 861. [14] J.W. Hunt, A.E. Worthington, A.T. Kerr, The subtleties of ultrasound images of an ensemble of cells: Simulation from regular and more random distributions of scatterers, Ultrasound in Medicine and Biology 21 (1995) 329. [15] G.R. Lockwood, L.K. Ryan, J.W. Hunt, F.S. Foster, Measurement of the ultrasonic properties of vascular tissues and blood from 35– 65 mhz, Ultrasound in Medicine and Biology 17 (1991) 653. [16] F.S. Foster, C.J. Pavlin, K.A. Harasiewicz, D.A. Christopher, D.H. Turnbull, Advances in ultrasound biomicroscopy, Ultrasound in Medicine and Biology 26 (2000) 1. [17] F.A. Duck, Physical Properties of Tissue, Academic Press Limited, London, 1990.
Intravascular ultrasound tissue harmonic imaging: A simulation study M.E. Frijlink a
a,*
, D.E. Goertz
a,b
, A. Bouakaz c, A.F.W. van der Steen
a,b
Biomedical Engineering, Erasmus MC, University Medical Center Rotterdam, The Netherlands b Interuniversity Cardiology Institute of the Netherlands, Utrecht, The Netherlands c Universite´ F. Rabelais, Tours, France Available online 30 June 2006
Abstract Recently, the in vivo feasibility of tissue harmonic imaging (THI) with a mechanically-rotated intravascular ultrasound (IVUS) catheter was experimentally demonstrated. To isolate the second harmonic signal content, both pulse inversion (PI) and analog filtering were used. In the present paper, we report the development of a simulation tool to investigate nonlinear IVUS beams and the influence of rotation on the efficiency of PI signal processing. Nonlinear 20 MHz beams were simulated in a homogeneous tissue-mimicking medium, resulting in second harmonic pressure fields at 40 MHz. The acoustic response from tissue was simulated by summing radio-frequency (RF) pulse–echo responses from many point-scatterers. When the transducer was rotated with respect to the point-scatterers, the fundamental frequency suppression using PI degraded rapidly with increasing inter-pulse angles. The results of this study will aid in the optimization of harmonic IVUS imaging systems. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Intravascular ultrasound; Nonlinear; Tissue harmonic imaging; Simulation
1. Introduction Intravascular ultrasound (IVUS) is capable of providing real time cross-sectional images of coronary arteries and, therefore, it has become an important clinical tool for the detection and evaluation of coronary artery diseases as well as for therapy guidance and clinical research [1]. At present, clinicians generally use rotating single-element IVUS catheters with center frequencies between 30 and 40 MHz. Tissue harmonic imaging (THI) has been shown to increase the diagnostic value of conventional echocardiography below 10 MHz by improving the image quality. We previously developed an experimental set-up to study the feasibility and potential of THI at IVUS frequencies. The suppression of stent imaging artifacts was shown when high frequency THI (transmit fc = 20 MHz, receive fc = 40 MHz) was applied in vitro [2]. More recently, we * Corresponding author. Present address: Thorax Center Ee23.02, Erasmus MC, PO Box 1738, 3000 DR Rotterdam, The Netherlands. Tel.: +31 10 4088031; fax: +31 10 4089445. E-mail address: [email protected] (M.E. Frijlink).
0041-624X/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2006.06.044
demonstrated in vivo the feasibility of THI for an IVUS system using a 20–40 MHz mechanically-rotated IVUS catheter [3]. In that study, tissue harmonic signals were isolated using a combination of analog filtering and pulseinversion (PI). The PI technique requires (at least) two firings of a pulse and its inverted counterpart for each acoustic line [4]. With tissue or catheter motion, the fundamental frequency signal (i.e., transmit bandwidth signal) is not completely cancelled, and the harmonic intensity becomes smaller due to signal misalignment. Motion artifacts of PI-based THI have been studied by Shen and Li [5]. Their results indicated that the tissue harmonic signal is significantly affected by tissue motion, and that for axial motion, the tissue harmonic intensity decreases much more rapidly than with lateral motion. This study was conducted under conditions relevant to low frequency array based scanning. A number of different approaches have been developed to model the nonlinear propagation in the field of an ultrasonic transducer [6]. The most common approach is to solve the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation, which is a nonlinear parabolic equation that
e186
M.E. Frijlink et al. / Ultrasonics 44 (2006) e185–e188
accounts for the combined effects of diffraction, absorption, and nonlinearity for directional sound beams [7]. Comparisons of nonlinear simulation results and measurements show excellent agreement [6],[8]. For relatively short pulses, as typically used in diagnostic ultrasound, the timedomain implementation of the KZK-equation is advantageous because many harmonic components could then be taken into account for the relatively broadband imaging pulses [7]. In this study, we simulated fundamental 20 MHz (F20), second harmonic (H40), and fundamental 40 MHz (F40) fields for an unfocused circular IVUS element using a two dimensional nonlinear parabolic KZK-equation and medium characteristics (attenuation, nonlinearity, scattering) in the range of those of vascular tissue and blood. The pulse–echo responses from point-scatterers, randomly positioned in three dimensions, were calculated for successive inverted pulses as the beam was rotated. The influence of rotation on the performance of PI was then investigated. 2. Methods 2.1. Simulation design The simulation of the transmitted nonlinear field by an unfocused circular transducer is based on a time-domain implementation of the KZK-equation based on Lee and Hamilton’s numerical approach [9]. The two dimensional implementation has been written in FORTRAN and has been previously evaluated [10]. The attenuation of acoustic waves propagating in a wide variety of lossy media obeys a power law dependence on frequency. The algorithm described by Bouakaz et al. [10] was modified to account for a frequency dependent attenuation different than a power law exponent of 2 (which corresponds to the power law exponent of attenuation of water). The received signal from an individual scatterer is calculated using an analytically derived spatial impulse response for an unfocused circular transducer [11]. In order to be able to use this spatial impulse response in combination with propagation in a frequency dependent attenuating medium, the distance from an individual point-scatterer to the piston transducer is approximated by a single value, similar to the approach described by Jensen et al. [12]. For the purpose of simulating ultrasound backscattered signals, tissue can be represented by many point scatterers positioned randomly in three dimensions [13],[14]. All point scatterers were assigned the same scattering strength and frequency dependent backscatter was taken into account. The backscatter signal from the cloud of scatterers is calculated by a summation of the individual responses from each scatterer. The scatterer density was sufficient to produce Rayleigh envelope statistics. The three-dimensional scatterer volume could be rotated with respect to the transmitted field to simulate catheter rotation of a mechanically scanned IVUS transducer.
2.2. Simulation parameters The nonlinear beams were calculated for a circular, unfocused transducer with a diameter of 0.9 mm, similar to IVUS elements used in previous IVUS THI studies [3]. Due to the circular symmetry, a two-dimensional simulation is sufficient to calculate three-dimensional fields. In all calculations, the excitation pulse was a Gaussian enveloped sine wave with a 30% fractional bandwidth. The propagation medium characteristics were chosen to be in the range of those of vascular tissue and blood. Arterial tissue and blood have a frequency dependent attenuation with power law exponents of 1.1 and 1.2, respectively, in the frequency range from 15 to 60 MHz [15],[16]. In the 10–50 MHz range, this is approximated by an attenuation that has a linear frequency dependency in the range from 0.5 to 1.5 dB/cm/MHz. In this study, a frequency dependent attenuation value of 1.0 dB/cm/MHz was used. The sound speed of the propagation medium was chosen to be 1560 m/s, the mass density 1050 kg/m3 and the nonlinear parameter (B/A) 6.0 [17]. The backscatter signal from the scatterers is calculated by the summation of responses from all scatterers that are within the 20 dB beamwidth. In our case, this means that all scatterers within a distance of 0.5 mm from the zaxis (corresponding to the propagation axis) are taken into account between z = 0.5 and z = 6.0 mm. Lockwood et al. [15] showed that the power law exponent of the frequency dependent backscatter in the artery wall ranged between c = 1.1 and 1.4, and that this parameter of blood ranged from c = 1.3 to 1.4 in the same frequency range. A frequency dependence of c = 1.3 has been chosen in this study. 2.3. Simulations 2.3.1. Nonlinear beam simulations Two-dimensional beam profiles were calculated in F20 and H40 mode for a maximum fundamental excitation pressure of 2 MPa. For comparison, a F40 beam profile was also calculated at a low excitation pressure of 50 kPa. 2.3.2. Effects of rotation on pulse inversion To study the effect of catheter rotation on the effectiveness of PI in suppressing fundamental frequency energy, two inverted 20 MHz pulses (0° and 180°) were propagated through the attenuating medium. Echoes from multiple point-scatterers have been calculated to simulate the RF pulse–echo responses at different angles with respect to the IVUS transducer. Fig. 1 shows the simulation set-up, showing the circular transducer and the point-scatterers. One data set consisting of 32 different realizations of a volume of randomly positioned scatterers was calculated for a F20 2 MPa amplitude pulse-pair. The average cross-correlation value between RF-lines was calculated as a function
M.E. Frijlink et al. / Ultrasonics 44 (2006) e185–e188
e187
Average cross-correlation between RF-lines [2-3 mm] raw RF H40 RF F40 RF
Cross-correlation
1 0.8 0.6 0.4 0.2 0 -0.2
α
Fig. 1. Schematic simulation set-up, showing randomly distributed pointscatterers in a 3D volume with respect to a rotating transducer.
of inter-pulse angle. This is done for both raw and filtered RF-lines (32–50 MHz, 5th order Butterworth). For comparison, the average cross-correlation for F40 RF-lines has also been calculated. The incremental inter-pulse angle was 0.15°, which corresponded to the experimentally employed line-density of 2400 RF-lines per rotation [3]. The effectiveness of PI for fundamental frequency suppression was studied at a distance of 2–3 mm from the transducer as a function of inter-pulse angle. The mean fundamental signal content of pulse-pairs was calculated by summing the frequency content between 18 and 22 MHz. 3. Results 3.1. Nonlinear beam simulations Two-dimensional beam profiles for F20, H40 and F40 modes are plotted in Fig. 2. These images are normalized
-4
-2 0 2 4 Inter-pulse angle [degrees]
6
Fig. 3. Cross-correlation between raw, H40 and F40 RF-lines at a distance from 2 to 3 mm from the transducer, plotted as a function of inter-pulse angle (in degrees).
with respect to the maximum signal within the individual images. The H40 beam shows less near field energy and a reduction in sidelobe energy compared to both F20 and F40. The attenuation of the medium causes the F40 to decay faster than both F20 and H40. 3.2. Effects of rotation on pulse inversion The average inter-pulse cross-correlation estimates for the raw, H40 and F40 RF-lines is given in Fig. 3 as a function of inter-pulse angle. These curves show the mean of 100 cross-correlation curves for windowed RF-lines corresponding to backscatter from 2 to 3 mm from the transducer. It can be seen that the cross-correlation peak is narrower for H40 and narrowest for F40, which is attributed to the beam width at this distance (Fig. 2). These curves indicate the legitimacy of averaging neighboring RF-lines to improve the signal-to-noise ratio (SNR) for small inter-pulse angles. For example, the decorrelation between H40 RF-lines (from 2 to 3 mm) is only <0.1 within an angle of 0.5°. The fundamental suppression through PI at a distance of 2–3 mm for the 2 MPa amplitude pulse-pair (0° and
Fig. 2. Two-dimensional beamprofiles in F20, H40 and F40 mode. The beamprofiles have been normalized with respect to the maximum signal within individual images.
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M.E. Frijlink et al. / Ultrasonics 44 (2006) e185–e188
Average fundamental reduction Fundamental suppression [dB]
30 25 20 15 10 5 0 0
2
4 6 8 Inter-pulse angle [degrees]
10
Fig. 4. The fundamental suppression with PI as a function of inter-pulse angle as calculated for a 2 MPa pulse-pair calculated for backscatter 2–3 mm from the transducer.
180°) is expressed as a function of inter-pulse angle in Fig. 4. This figure shows that the fundamental suppression decreases rapidly with increasing inter-pulse angles, which is linked to the reduced cross-correlation between raw F20 RF-lines for increasing inter-pulse angles (Fig. 3). Thus, a reduced line-density corresponding to an increased inter-pulse angle, leads to a reduced fundamental suppression when PI is applied. Fig. 4 indicates a fundamental suppression of 16 and 10 dB when PI is applied with an interpulse angle of 0.70° and 1.4°, respectively, corresponding to approximately 512 and 256 RF-lines per rotation. These line-densities correspond to those used in current clinical mechanically scanned IVUS systems. 4. Conclusion and discussion Nonlinear fields at 20–40 MHz have been simulated for circular IVUS transducers through media with frequency dependent attenuation values in the range of those of vascular tissue and blood. The influence of transducer rotation on the fundamental suppression of pulse inversion has been studied for a range of inter-pulse angles. In the simulations with a rotating transducer, the minimal inter-pulse angle was chosen to be 0.15°, based on a line-density of 2400 lines per rotation. Using this line-density, the commercially and clinically used rotational speed of thirty rotations per second will than result in a pulse-repetition-frequency (PRF) of approximately 75 kHz, which is still lower than the maximum PRF of a rotating single-element IVUS system as limited by sound propagation speed. So in spite of a lower line-density (e.g., 256 lines per rotation) at 30 rotations per second of current commercially available IVUS systems, no physical limitations exist to increase to a line-density of 2400 lines per rotation. A degradation of fundamental suppression with PI was observed for increasing inter-pulse angles. This is due to increased decorrelation between RF pulse-pairs for increas-
ing inter-pulse angles. Future simulations might gain insight in the competing effects of decorrelation and pulse averaging, resulting in a trade-off between SNR and resolution. The results from this simulation study will guide the optimization of harmonic IVUS systems with mechanically scanned single-element catheters. The PRF, line-density and transducer size and geometry could be altered to optimize the fundamental suppression with PI. This simulation tool could also be used to investigate different pulse schemes (coded excitation) for isolating harmonic signals. Further, such simulations may also be useful in the context of guiding the implementation and optimization of nonlinear contrast imaging systems. References [1] Y. Saijo, A.F.W. van der Steen, Vascular Ultrasound, SpringerVerlag, Tokyo, 2003. [2] M.E. Frijlink, D.E. Goertz, A.F.W. van der Steen, Reduction of stent artifacts using high-frequency harmonic ultrasound imaging, Ultrasound in Medicine and Biology 31 (2005) 1335. [3] M.E. Frijlink, D.E. Goertz, L.C.A. van Damme, R. Krams, A.F.W. van der Steen, Intravascular ultrasound tissue harmonic imaging in vivo, IEEE Ultrasonics Symposium (2004) 1118. [4] D.H. Simpson, C.T. Chin, P.N. Burns, Pulse inversion doppler: A new method for detecting nonlinear echoes from microbubble contrast agents, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 46 (1999) 372. [5] C.C. Shen, P.C. Li, Motion artifacts of pulse inversion-based tissue harmonic imaging, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 49 (2002) 1203. [6] V.F. Humphrey, Nonlinear propagation in ultrasonic fields: Measurements, modelling and harmonic imaging, Ultrasonics 38 (2000) 267. [7] M.F. Hamilton, D.T. Blackstock, Nonlinear Acoustics, Academic Press, San Diego, 1998. [8] F.A. Duck, Nonlinear acoustics in diagnostic ultrasound, Ultrasound in Medicine and Biology 28 (2002) 1. [9] Y.S. Lee, M.F. Hamilton, Time-domain modeling of pulsed finiteamplitude sound beams, Journal of the Acoustical Society of America 97 (1995) 906. [10] A. Bouakaz, C.T. Lancee, N. de Jong, Harmonic ultrasonic field of medical phased arrays: Simulations and measurements, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 50 (2003) 730. [11] P.R. Stephanishen, Transient radiation from pistons in an infinite planar baffle, Journal of the Acoustical Society of America 49 (1971) 1629. [12] J.A. Jensen, D. Gandhi, W.D. O’Brien, Ultrasound fields in an attenuating medium, IEEE Ultrasonics Symposium (1993) 943. [13] A.T. Kerr, J.W. Hunt, A method for computer simulation of ultrasound doppler color flow images-i. Theory and numerical method, Ultrasound in Medicine and Biology 18 (1992) 861. [14] J.W. Hunt, A.E. Worthington, A.T. Kerr, The subtleties of ultrasound images of an ensemble of cells: Simulation from regular and more random distributions of scatterers, Ultrasound in Medicine and Biology 21 (1995) 329. [15] G.R. Lockwood, L.K. Ryan, J.W. Hunt, F.S. Foster, Measurement of the ultrasonic properties of vascular tissues and blood from 35– 65 mhz, Ultrasound in Medicine and Biology 17 (1991) 653. [16] F.S. Foster, C.J. Pavlin, K.A. Harasiewicz, D.A. Christopher, D.H. Turnbull, Advances in ultrasound biomicroscopy, Ultrasound in Medicine and Biology 26 (2000) 1. [17] F.A. Duck, Physical Properties of Tissue, Academic Press Limited, London, 1990.