Nonlinear Propagation of Ultrasound Through ... - IEEE Xplore

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ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 53, no. 12, december 2006

Nonlinear Propagation of Ultrasound Through Microbubble Contrast Agents and Implications for Imaging Meng-Xing Tang, Member, IEEE, and Robert J. Eckersley, Member, IEEE Abstract—Microbubble contrast agents produce nonlinear echoes under ultrasound insonation, and current imaging techniques detect these nonlinear echoes to generate contrast agent images accordingly. For these techniques, there is a potential problem in that bubbles along the ultrasound transmission path between transducer and target can alter the ultrasound transmission nonlinearly and contribute to the nonlinear echoes. This can lead to imaging artefacts, especially in regions at depth. In this paper we provide insight, through both simulation and experimental measurement, into the nonlinear propagation caused by microbubbles and the implications for current imaging techniques. A series of investigations at frequencies below, at, and above the resonance frequency of microbubbles were performed. Three specific effects on the pulse propagation (i.e., amplitude attenuation, phase changes, and harmonic generation) were studied. It was found that all these effects are dependent on the initial pulse amplitude, and their dependence on the initial phase of the pulse is shown to be insignificant. Two types of imaging errors are shown to result from this nonlinear propagation: first, that tissue can be misclassified as microbubbles; second, the concentration of microbubbles in the image can be misrepresented. It is found that these imaging errors are significant for all three pulse frequencies when the pulses transmit through a microbubble suspension of 6 cm in path length. It also is found that the first type of error is larger at the bubble resonance frequency.

I. Introduction range of techniques has been developed for detection of microbubble contrast agents in vivo using ultrasound (US). Examples include: pulse inversion (PI), amplitude modulation (AM), and a combination of the two, i.e., pulse inversion amplitude modulation (PIAM) [1]–[4]. These techniques make use of the nonlinear behavior of the microbubbles under ultrasound insonation. Typically, multiple pulses are used, and their echoes combined to remove the signal from linear scatterers while preserving that from

A

Manuscript received June 2, 2006; accepted July 7, 2006. MengXing Tang is supported by the EPSRC(EP/C536150/1). Robert J. Eckersley is funded by the EPSRC (Grant no. GR/S71224/01). The authors also would like to thank MIAS-IRC (UK EPSRC grant GR/N14248/01 and UK Medical Research Council grant no. D2025/31) for their support. M.-X. Tang is with the Department of Bioengineering, Faculty of Engineering, Imperial College London, London, SW7 2AZ, UK (email: [email protected]). R. J. Eckersley is with the Imaging Sciences Department, Faculty of Medicine, Imperial College London, London, W12 0HS, UK. Digital Object Identifier 10.1109/TUFFC.2006.189

the nonlinear microbubbles. Although these techniques are successful in improving the detection sensitivity for microbubbles, there is a problem that has been largely ignored so far; before reaching the target, the ultrasound insonation signal already may have propagated through a nonlinear medium containing both bubbles and tissues. In this case, not only the bubbles at the target but also the bubbles along the transmission path will contribute to the nonlinearity of the received echoes. This process potentially can lead to imaging artefacts, especially in regions at depth. A range of mechanisms can alter the transmission signal during the interaction of the ultrasound with microbubbles. Generally, these interactions are covered by the processes involved in absorption and scattering. Furthermore, the speed of sound can be altered by the presence of bubbles. Although most media are able to change ultrasound transmission through absorption, scattering and changing speed of sound, microbubbles oscillate in a very nonlinear way, and the resultant changes in transmission are in general nonlinear. Previous research on this topic is limited. Hamilton and Blackstock [5] have studied the nonlinear propagation theoretically using simplified models consisting of a wave equation coupled with a RayleighPlesset equation. In this analysis, they describe the effect of bubbles in a medium on the index of nonlinearity (B/A). They found that a moderate concentration of microbubbles can increase B/A from 5 to as high as 3000 for frequencies below the resonance frequency, but the increase in B/A is minimal for frequencies above the resonance frequencies. De Jong [6] has experimentally measured B/A of US pulses at 1 MHz and 2 MHz transmitted through Isoton (Coulter Electronics Ltd., Luton, England, UK) and through Albunex (Nycomed AS, Oslo, Norway) contrast agent suspension. He found that B/A for both frequencies was much higher when the pulse was transmitted through Albunex suspension. However, few studies have reported on the nonlinearities from an imaging perspective. At the same time, there has been no report quantitatively evaluating the imaging error caused by this nonlinear propagation. The interaction between the ultrasound signal and microbubbles (i.e., the absorption and scattering of ultrasound) results in the attenuation of the ultrasound transmission. Chen et al. [7] reported experimental observations that the attenuation of ultrasound transmission amplitude by microbubbles is nonlinear and dependent on the in-

c 2006 IEEE 0885–3010/$20.00

tang and eckersley: propagation of ultrasound, microbubble contrast agents, and implications for imaging

Fig. 1. Diagram for the ultrasound measurement system.

sonation acoustic pressure. In a previous paper [8] we proposed a nonlinear attenuation model and experimentally demonstrated the amplitude dependence of attenuation. This amplitude dependence could have consequences for multipulse nonlinear imaging sequences using amplitude modulation. In our previous paper [8], we did not consider the effect of incident phase of the pulse on attenuation. In an ideal linear medium, the phase change at a specific frequency depends only on the medium itself, but further studies are needed for microbubbles as to whether this phase change depends on the pulse parameters such as the initial amplitude and phase. Because nonlinear imaging techniques use pulses of various amplitude and phase, any dependence of phase change during transmission on amplitude or phase also would result in imaging errors. In addition to the nonlinear changes to amplitude and phase of the transmitted signal at the original center frequency, additional harmonic signals are generated during propagation through a suspension of microbubbles. These could cause further imaging errors because these harmonics also are generated by microbubbles on the transmission path. In this paper, both theoretical and experimental methods are used to explore the nonlinear propagation of ultrasound transmission through microbubbles from an imaging perspective and to illustrate and quantify imaging errors caused by this nonlinear propagation.

II. Methods A. Transmission Measurements by Single-Element Transducers The nonlinear propagation of ultrasound transmission through microbubbles was studied using ultrasound transmission measurements through a bulk volume of a microbubble suspension. SonoVueTM (Bracco S.p.A., Milan, Italy) was diluted in saline (0.9%, w/v) and insonated using a laboratory ultrasound measurement system. A diagram of this system is shown in Fig. 1. Three transducers with nominal central frequency of 0.5 MHz, 2.75 MHz, and 3.5 MHz were used for transmissions (Videoscan,

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Panametrics-NDT, Waltham, MA). Each transducer consists of a single element with a 3-cm aperture and is geometrically focused to 7.5 cm, with the exception of the 0.5 MHz transducer, which is focused to 4 cm. A calibrated needle hydrophone (Precision Acoustics Ltd., Dorchester, UK) was positioned on the axis of the beam 1 cm behind the focus of the transducer in each case. All the experiments were performed in a large water bath maintained at 37◦ C. Four narrowband pulses (with two peak negative pressure levels, 64 kPa and 32 kPa, and two phases, 0 and 180 degrees) were transmitted through the bubble suspension. These four pulses are referred to as +1 (64 kPa, zero phase), −1/2 (32 kPa, 180 phase), −1 (64 kPa, 180 phase), and +1/2 (32 kPa, zero phase). Each narrowband pulse consists of a Gaussian enveloped sinusoidal signal of 16 cycles. Studies using such narrowband pulses are able to separate effects of harmonic generation from changes at fundamental frequencies. In addition, broadband pulses with two sinusoidal cycles also were used as comparison. There was a 1 s delay between consecutive pulses. The use of low-acoustic pressure reduces the chances of both bubble disruption and nonlinear propagation in water. Transmission measurements were made with a bubble concentration of 230 µl/1000 ml, which is in the same range as that found in the blood pool of a patient when used clinically. The sample chambers used here have an acoustic path length of 6 cm. For every measurement with microbubbles, an identical bubble-free control measurement was made. Three central frequencies for transmission pulses, 0.5 MHz, 1.75 MHz, and 3.5 MHz, were used in the experiments. These frequencies are below, near and above the resonance frequency of the SonoVueTM suspension. The resonance frequency of 1.75 MHz was experimentally determined through multiple, narrowband transmission measurements at the beginning of this study. The experimental data were used for two purposes. To illustrate and analyze the complex process of nonlinear propagation through microbubbles with respect to nonlinear amplitude attenuation, nonlinear phase changes and harmonic generation. Here the attenuation and phase changes are calculated at each frequency point on the spectrum of the pulses. It should be noted that, unlike attenuation or phase change, which can be linear or nonlinear, harmonic generation is inherently nonlinear. Second, the data were used in combination with a simulation of bubble scattering, to evaluate potential imaging errors caused by this nonlinear propagation with multiple-pulse imaging techniques such as PI, AM, and PIAM. B. Theoretical Methods 1. Simulation of Nonlinear Propagation: The simulation was based on the following wave equation [5]: ∇2 p(x, t) −

1 ∂ 2 p(x, t) ∂ 2 v(x, t) = −ρ0 N , 2 2 c0 ∂t ∂t2

(1)

where p(x, t) is the acoustic pressure, ρ0 is the ambient density of the medium, v(x, t) is the volume change of a

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ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 53, no. 12, december 2006 TABLE I Model Parameters.

TABLE II The Four Combinations of Linear/Nonlinear Propagation and Scatterers Simulated and Studied Experimentally.

Parameters

Values

pl0 : Ambient pressure pv : Vapor pressure ρ: Density of liquid µ: Viscosity in liquid c: Speed of sound in liquid Γ: Polytropic exponent of the gas Sp : Shell elasticity parameter Sf : Shell friction parameter σ: Surface tension

1.01e5 N·m−2 2.33e3 N·m−2 1000 kg·m−3 1.0e-3 N·s·m−2 1500 m·s−1 1.4 1.1 N·m−1 0.45e-6 Kg·s−1 0.072 N·m−1

single microbubble during oscillation. Hamilton and Blackstock [5] assumed that the medium contains a spatially uniform distribution of N identical bubbles that are small compared with a wavelength. In [9] this has been extended to microbubbles of a size distribution n(R0 ). The right hand side (RHS) of (1) can be rewritten as: ⎡ ⎤ ∞ 4 ∂ 2 ⎣ π R03 n (R0 ) dR0 ⎦ 3 2 ∂ V (x, t) 0 = −ρ0 −ρ0 ∂t2 ∂t2 ∞ (2) ¨ 0 n (R0 ) dR0 , = −ρ0 4π 2R0 R˙ 02 + R02 R 0

and (1) becomes: 1 ∂2p ∇ p − 2 2 = −ρ0 4π c0 ∂t 2

∞ 0

¨ 0 n (R0 ) dR0 . 2R0 R˙ 02 + R02 R (3)

To solve this equation, the values of bubble radius R0 and its derivatives over time need to be calculated. This was done using the modified Rayleigh, Plesset, Noltingk, Neppiras and Poritsky (RPNNP) equation where shell elasticity Sp and shell friction Sf parameterize the bubble: 3Γ 3 ˙2 R0 ¨ ρRR + ρR = pg0 + pv − pl0 2 R 2σ 1 1 − − 2Sp − − δt ωρRR˙ − pac (t), (4) R R0 R where R is the instantaneous bubble radius; R0 is the equilibrium bubble radius; pg0 is the initial gas pressure inside the bubble; δt is the total damping coefficient, which includes radiation damping δrad , viscosity damping, δvis , thermal damping, δth and shell friction damping δf ; ω is the angular frequency of incident acoustic field; pac (t) is the incident acoustic pressure. Description of other parameters and their values are presented in Table I. The bubble shell parameters used in this simulation follow that in [10], and the remaining model parameters follow those in de Jong et al. [11]. The numerical implementation of the simulation was conducted for a homogeneous microbubble suspension in

Case

Transmission

Target

A B C D

Linear (tissue) Linear (tissue) Nonlinear (microbubbles) Nonlinear (microbubbles)

Linear (tissue) Nonlinear (microbubbles) Linear (tissue) Nonlinear (microbubbles)

one spatial dimension and temporal dimension to obtain the pressure field p(t, x). The implementation followed that described in [9] in which (3) is discretized based on a grid spanning both space and time. The modified RPNNP equation is coupled to the wave equation through (3). For each grid point (i, j) in space and time, (3) is solved for pressure p(i, j), given the RHS of (1). Then p(i, j) is used in (4) as incident acoustic pressure to calculate at this point the bubble status R(i, j) and its derivatives. This (4) was solved for each bubble size, and the calculated quantities such as radius and derivatives of radius, together with the information of bubble size distribution, were input into (2) to obtain the RHS of (1) for the next iteration. The size distribution of the bubbles was taken from [10]. The pressure radiated by the bubble then was calculated using the following [12]: ρ ¨ . ps (t) = (5) 2RR˙ 2 + R2 R r Multiple simulations were carried out using different insonating pulses with frequencies below, at, and above the resonance frequency of the microbubbles, similar to those pulses used in the experimental measurements described previously. Results were compared to those obtained experimentally. 2. Evaluation of Imaging Errors Caused by the Nonlinear Propagation: The potential imaging errors consist of two types: Type-1, tissue can be misclassified as microbubbles; and Type-2, the nonlinear propagation induces changes in signal intensity so the concentration of microbubbles in the image is misrepresented. These two types of imaging errors were evaluated by studying four imaging cases summarized in Table II. In Table II linear transmission means the signal is transmitted through approximately linear attenuators such as tissue, and the signal amplitude is linearly attenuated. In this case, an experimentally measured control data was used as the insonation signal. For US transmission through microbubbles, experimentally measured data was used. For the linear target, the incident signal simply was scaled, and for microbubble target, the modified RPNNP model in (4) was used to calculate the scattered signal for a single bubble with a radius of 3 µm. For each case shown in Table II, the scattered signals for the four pulses (i.e., +1, −0.5, −1, +0.5) were obtained. In order to evaluate imaging errors, the residual signal


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III. Results and Discussion A. Experimental Data Analysis

Fig. 2. Phantom consisting of a compartment filled with microbubbles on top of a block of tissue-mimicking material.

is calculated by cancelling out the linear components of the scattered signals for each of the four cases defined in Table II. In Case A, there was no nonlinear propagation and no bubbles at the target; therefore, complete cancellation is expected for any of the pulsing schemes (i.e., PI, AM, and PIAM). In Case B, the residual power should correspond to the target-scattering bubble only. Case C shows the undesired residual (i.e., imaging error) due to nonlinear propagation through bubble when the target is linear. The residual in case D includes both the desired nonlinear component from target bubbles and the undesired component from bubbles on the transmission path. Difference in residuals between Case A and Case C provides a measure of the nonlinear propagation-induced errors in misclassification of tissue as microbubbles, here defined as Type-1 errors. Difference in residuals between Case B and D provide a measure of additional errors in image intensity induced by nonlinear propagation, here defined as Type-2 errors. Note that, in this paper, the residuals are always quoted as the square root of residual power normalized by the total scattering power of the pulse pair before linear cancellation. Type-1 and Type-2 errors are calculated for three nonlinear imaging techniques (PI, AM, and PIAM), three insonating central frequencies (0.5, 1.75, and 3.5 MHz) and two pulse lengths (2 cycles and 16 cycles). C. Visualization of Imaging Artefacts with a US Scanner A US system (ACUSON Sequoia 512, Siemens Medical Solutions, Berkshire, UK) was used to demonstrate the errors caused by the nonlinear propagation in a clinical ultrasound system. A phantom was made consisting of a compartment filled with microbubbles on top of a block of tissue-mimicking material (agar gel with a suspension of cellulose particles) (Fig. 2). The thickness of both the bubble compartment and tissue mimicking material is 20 mm. A contrast specific image (CPS) of the phantom was obtained before and after the administration of a dose equivalent to 150 µl/ of microbubbles. Because the compartment lies on top of the tissue-mimicking phantom, the bubbles in the compartment can corrupt the signal to and from the tissue-mimicking material. Comparing the prebubble control image with the postbubble measurement allows visualization of the imaging artefacts due to nonlinear propagation.

The results of the experimental study are presented in Fig. 3. This figure shows, in the frequency domain, the three nonlinear propagation effects due to the microbubbles, i.e., amplitude attenuation (top row), phase changes (middle row), and second harmonic generation (bottom row) for the four narrowband pulses (+1, −1, +0.5, and −0.5). Each curve in Fig. 3 corresponds to a particular insonation pulse used. In each graph in Fig. 3, the amplitude attenuation and phase change due to bubbles were calculated with reference to the bubble-free control measurements. The second harmonics, shown in Fig. 3(g), (h), (i), were normalized within each graph by the fundamental peak for pulse +1. It should be noted that only narrowband results are shown here because, when broadband pulses are used, it is harder to separate effects of changes at the fundamental frequency from harmonic generation. It can be seen that there is a significant dependence on the initial insonating amplitude of attenuation, phase change and harmonic generation. This dependence will cause imaging errors when insonating with pulses of different amplitude, such as in AM. At the same time, it can be seen that the curves for each of the three effects generally overlap when the same initial insonating amplitude is used; the curves of pulse +1 overlap with those of pulse −1 and the same is true for pulse +0.5 and −0.5. Such overlapping suggests no dependence of amplitude attenuation, phase change, or harmonic generation on the initial insonating phase. Consequently, if an imaging technique involving pulses of equal amplitude but different phase such as PI is used, the effects of attenuation and phase changes for the pulse pair will cancel out and, therefore, will not affect the imaging results. For the second harmonics generated, they will always add up during linear cancellation and cause imaging errors. It can be seen that the dependence of attenuation on insonation pulse amplitude, as characterized by the difference between the upper and lower curves in Fig. 3(a), (b), (c), is most significant around the resonant frequency. The average difference in attenuation between full amplitude insonation (pulse +1 and −1) and half amplitude insonation (pulse +0.5 and −0.5) is more than 4 dB at resonance frequency in Fig. 3(b), but only 2 dB at 0.5 MHz in Fig. 3(a) and 1 dB at 3.5 MHz in Fig. 3(c). The amplitude of the second harmonic signal is shown to be most significant for insonation nearer the resonant frequency, as shown in Fig. 3(h) and, consequently, should cause more imaging errors at this frequency. The amplitude of the second harmonic signal for insonation below resonance in Fig. 3(g) is slightly less than that at resonance in Fig. 3(h), but it is much higher than insonation above resonance in Fig. 3(i). This is consistent with Hamilton and Blackstock’s study [5] in which the second harmonic generation is shown to be very significant only for frequencies below and at the resonance frequency. However, they described a much larger decrease (approximately −55 dB) in

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Fig. 3. Amplitude attenuation, phase changes, and second harmonic generation for different insonating pulses. Top row, amplitude attenuation; middle row, phase changes (note the origin change in different figures); bottom row, second harmonic generation (normalized); left column, insonation at frequency below resonance (0.5 MHz); middle column, insonation at resonance frequency (1.75 MHz); right column, insonation at frequency above resonance (3.5 MHz).

second harmonic generation when the frequency increases beyond resonance. One possible explanation for this is that Hamilton and Blackstock only analyzed a single-sized bubble population, and the experimental results in this study came from bubble suspension with a size distribution in which there are a proportion of bubbles resonant at 3.5 MHz. The dependence of the phase of the transmitted pulse on the insonating pulse frequency also is seen in Fig. 3. Changing from a negative phase shift below the resonance of the microbubbles through to positive at frequencies higher than the resonant frequency, both the full amplitude and the half amplitude pulses exhibit a similar trend. At frequencies near to resonance, the phase change is close

to zero. Note, it is the change in phase speed that is displayed, rather than the phase speed itself. For phase speed there should be a sudden change near resonance frequency as described in [5]. Key factors that determine the amplitude of nonlinear propagation include the bubble concentration in the region and the depth of the region of interest. Higher concentration or deeper target will result in more nonlinear propagation. The bubble concentration used in this study corresponds to that in blood pool in a typical clinical investigation. The depth of the target in this study is 6 cm, which is the length of the acoustic path through the beaker in the experimental measurements. In clinical cases for imaging tissue with blood perfusion, the bubble concentration


(a)

(b)

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(c)

Fig. 4. Comparing results of propagation simulation using a bubble-size distribution with real data. (a) 0.5 MHz; (b) 1.75 MHz; (c) 3.5 MHz.

within the tissue could be much less than that in the blood pool. Therefore, the imaging errors at 6 cm away from the transducer will be less than that predicted in this study, but these errors will increase with depth and bubble concentration. B. Simulation of Nonlinear Propagation Fig. 4 shows the simulation results compared to experimental results for ultrasound propagation through microbubble suspension with three different frequencies. It can be seen that, within the fundamental frequency range, the simulation in general corresponds well to the real data for each measurement. The small discrepancies within this frequency range could be due to any differences in bubble size distribution between our experiment and that described in [10]. However, a significant difference between simulation and real data exist at harmonic frequencies. In the real data, there is significant harmonic generation, but in simulation there is hardly any (Fig. 4). Furthermore, for the simulation conducted with different initial pulse amplitudes, the results did not show any significant dependence of either attenuation or phase change on the initial pulse amplitude. In brief, the simulation does not show significant nonlinearity during the propagation through a microbubble cloud. There are key assumptions in the propagation model used for simulation, which are likely to cause the discrepancies between simulation and real data. The model consists of two coupled differential equations, i.e., the inhomogeneous wave equation and the modified RPNNP equation. In the wave equation (1), it is assumed that the medium contains a spatially uniform distribution of small bubbles and can be treated approximately as a homogeneous medium. As a result of this assumption, the nonlinear responses of bubbles with different sizes are linearly summed up, then averaged using (2) to calculate the RHS of (1). This linear averaging of nonlinear signals is likely to contribute to the reduction of nonlinearity in the simulation. To investigate this further, an additional simulation was conducted using bubbles of a uniform size as opposed to the distribution used above. In this case, bubbles of 3 µ in radius were insonated at a frequency of 1.75 MHz. As

Fig. 5. Comparing results of propagation simulation using bubbles of a single size (3 µ in radius) with real data. Pulse central frequency, 1.75 MHz.

shown in Fig. 5, increased harmonics occur after the simulation propagation. Due to a lack of bubble size distribution, the spectrum of the simulation data shows a significant loss of power in a narrow band, corresponding to the resonance frequency of the 3-µ sized bubbles. Further studies are needed to improve the propagation simulation and produce more realistic simulation results. This would be a vital tool to further characterize the nonlinear propagation and to help develop correction methods for imaging artefacts caused by this nonlinear propagation. C. Evaluation of Imaging Errors The imaging errors caused by the nonlinear propagation through microbubbles were evaluated for the three nonlinear imaging techniques: PI, AM, and PIAM. Results for the four cases defined in Table II with a narrowband transmission centered at 1.75 MHz are presented in Fig. 6 for one of these techniques: PIAM. The measured residual signal after linear cancellation, normalized to the total echo power, also is presented in Fig. 6.

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Fig. 6. Evaluation of imaging errors in PIAM for the four cases defined in Table II. Scattered signals and residual signals after combination are shown in both temporal domain (a), (c), (e), (g) and frequency domain (b), (d), (f), (h). The numbers below (a), (c), (e), (g) shown in decibels are the power of residual signals with reference to the total scattered power of pulse + 1.


Fig. 6(a) shows good cancellation of the two scattering signals for pulse +1 and −0.5 when both the transmission and the target are linear. In the frequency spectrum Fig. 6(b) there is only a small amount of fundamental and second harmonic components in the residual, which is likely due to nonlinear propagation in water during the control measurement. The total residual power after cancellation is at −28.3 dB relative to the total scattering power. Fig. 6(c) shows the residual signal arising from a microbubble target while the transmission is linear. This residual power after combination of the two scattering signals for pulse +1 and −0.5 is about −8.48 dB of the scattering signals. In the spectrum in Fig. 6(d), there are significant fundamental as well as second and third harmonic components, which corresponds well to the theoretical prediction in PIAM. Fig. 6(e) shows the residual signal, or imaging error, when the target is linear but the transmission is nonlinear due to microbubbles. In this case, when the target is linear, the residual power is at −1.69 dB relative to the total scattered power. Comparing this with Fig. 6(a) shows a 26.6 dB increase in the residual power due to nonlinear propagation through microbubbles. This significant residual power for a linear target in this case means this would be misclassified as bubbles. The spectrum in Fig. 6(f) shows that the nonlinear propagation introduced both significant fundamental and second harmonic components. Fig. 6(g) shows the case in which both transmission and scattering are nonlinear. In this case, the residual signal after linear cancellation contains both the desired residual signal from target bubbles and the undesired residual signal due to nonlinear propagation. The residual power is −1.94 dB of the scattered signal. Comparing this with case Fig. 6(c) shows that the nonlinear propagation increased the residual power by 6.54 dB in this case. Fig. 7 shows a summary of the two types of imaging errors for both long insonating pulses and shorter, more typical, imaging pulses. Generally, it can be seen that Type1 errors (i.e., tissue being identified as bubbles) are significantly higher when insonated near the resonance frequency. This is expected because more bubbles resonate around this frequency that introduces more nonlinearity into the transmission pulse. The errors at 0.5 MHz and 3.5 MHz also are significant, with that of 0.5 MHz being higher. Two factors have contributed to this. One is that there also are a significant number of bubbles resonant around these two frequencies. The other is that nonlinearity at frequency below resonance is much greater than above resonance, as described in Hamilton and Blackstock’s study [5]. For Type-2 errors, the general trend is quite different and shows a decreasing error with increasing frequency. One difference between the Type-1 and Type2 errors is that, for Type-2 errors, the target consists of bubbles. Because the imaging errors are defined as erroneous residual normalized by the total scattering power from target, the errors are reduced at resonance frequency

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Fig. 7. Imaging errors caused by nonlinear propagation through a microbubble suspension of 6 cm in length. The errors shown are the difference in residuals between linear propagation cases and nonlinear propagation cases. Note that the residuals are quoted as the square root of residual power normalized by the total scattering power of the pulse pair before linear cancellation.

by this normalization because of higher total scattering power from the target bubbles at resonance frequency. Furthermore, for evaluating Type-2 errors, only a single-sized bubble of 3 µm radius is used to calculating the scattering signals. This can give unrealistically small bubble scattering and exaggerate this type of imaging errors at offresonance frequencies. It should be noted that, because equal amplitude pulses are used in PI, nonlinear attenuation or phase changes at a fundamental frequency band are not contributing to imaging errors and the main contribution must come from harmonic generation. As a result, it is expected that imaging errors in PI would be lower than those in AM and PIAM. However, Fig. 6 does not show any reduced errors for PI. Instead, in some cases, PI shows higher imaging errors than AM and PIAM. This is probably due to the lower amplitude of one of the pulses in both AM and PIAM. For theses lower amplitude pulses, the harmonic generation during nonlinear propagation is significantly less, and the overall imaging errors are reduced to a level similar to that from PI in this case. It also should be noted that, during the above analysis, the residuals in AM and PIAM could be artificially ampli-

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(a)

(b)

Fig. 8. Visualization of imaging artefacts due to nonlinear propagation with a commercial US scanner. (a) The tissue mimicking material shows little nonlinear signal before bubbles are injected into the above compartment. (b) The same tissue-mimicking material shows significant nonlinear signal after bubbles are injected.

fied due to the fact that the smaller one of the pulse pair is always multiplied by two before linear cancellation, but in PI there is no such multiplication. Furthermore, imaging errors due to nonlinear propagation at 500 kHz may have been overestimated in this study as the experimental measurements were made with microbubbles in a beaker, thus more large-sized bubbles may have been present compared to the in-vivo case in which these large-sized bubbles would be removed by the pulmonary circulation. Fig. 8 shows the imaging artefacts due to nonlinear propagation using a commercial US scanner. In Fig. 8(a), before bubbles are injected, the nonlinear signal from tissue mimicking material is weak, but in Fig. 8(b) when bubbles are present the same tissue mimicking material shows a much stronger nonlinear signal and could be misclassified as bubbles. IV. Conclusions It has been shown that nonlinear propagation through a microbubble suspension can be significant. This not only induces changes in the echoes from bubbles and introduces errors in the resulting image intensity, but it also can cause misrepresentation of deeper linear scattering structures as nonlinear scatterers. It has been shown that the imaging artefacts due to this nonlinear propagation can be significant. At present all multipulse detection techniques are unable to distinguish the echoes from linear scatterers (corrupted by propagation) and from the true nonlinear scattering microbubble contrast agents. This also has implications for image-based quantification of microbubble contrast studies. The results of imaging error evaluation have shown that both imaging Type-1 errors (i.e., tissue being identified as bubbles) and imaging Type-2 errors (i.e., concentration of microbubbles is misrepresented) are significant at all the three insonating frequencies used. Type-1 error has a peak at resonance frequency, but for Type-2 errors further studies are needed to evaluate their relationship with frequency.

Nonlinear propagation of an ultrasound pulse can be shown in terms of nonlinear amplitude attenuation, nonlinear phase changes, and generation of new harmonic components during the transmission, all of which are shown to be dependent on the initial insonating acoustic pressure. At the same time, they also depend on the insonating frequency. The amplitude attenuation and phase change are independent on initial insonating phase. The simulation of nonlinear propagation is found to be fairly consistent with experimental measurements, but further study is needed to achieve a better consistency. In this paper, we have gained insight into this problem although it is yet to be solved. The end goal of this study should be the design of appropriate correction techniques so that better detection in deep tissue and quantification of contrast images can be obtained. Previously we presented initial steps toward compensation of nonlinear attenuation of the microbubbles [8]. However, our previous approach considered only nonlinear amplitude attenuation. A more realistic simulation of nonlinear propagation is required to provide a vital tool to further characterize the nonlinear propagation and to assist in developing robust correction methods for the imaging artefacts. Acknowledgment The authors would like to thank the anonymous referees for their extremely useful suggestions. The authors would also like to thank Professor J. Alison Noble, Professor David Cosgrove, Mr. Kevin Chetty, Dr. Eleanor Stride, and Miss Kathryn Hibbs for their help and useful suggestions. References [1] D. H. Simpson, P. N. Burns, and M. A. Averkiou, “Techniques for perfusion imaging with microbubble contrast agents,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 48, pp. 1483– 1494, 2001. [2] M. Averkiou, “Ultrasonic nonlinear imaging at fundamental frequencies,” U.S. Patent 6,319,203, 2001.

tang and eckersley: propagation of ultrasound, microbubble contrast agents, and implications for imaging [3] P. J. Phillips, “Contrast pulse sequences (CPS): Imaging nonlinear microbubbles,” in Proc. IEEE Ultrason. Symp., vol. 2, 2001, pp. 1739–1745. [4] R. J. Eckersley, C. T. Chin, and P. N. Burns, “Optimising phase and amplitude modulation schemes for imaging microbubble contrast agents at low acoustic power,” Ultrasound Med. Biol., vol. 31, no. 2, pp. 213–219, 2005. [5] M. F. Hamilton and D. T. Blackstock, Non-linear Acoustics. New York: Academic, 1998. [6] N. de Jong, “Acoustic properties of ultrasound contrast agents,” Ph.D. dissertation, Erasmus University Rotterdam, Rotterdam, The Netherlands, 1993. [7] Q. Chen, J. Zagzebski, T. Wilson, and T. Stiles, “Pressuredependent attenuation in ultrasound contrast agents,” Ultrasound Med. Biol., vol. 28, no. 8, pp. 1041–1051, 2002. [8] M.-X. Tang, R. J. Eckersley, and J. A. Noble, “Pressuredependent attenuation with microbubbles at low mechanical index,” Ultrasound Med. Biol., vol. 31, no. 3, pp. 377–384, 2005. [9] E. Stride and N. Saffari, “Investigating the significance of multiple scattering in ultrasound contrast agent particle populations,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 52, no. 12, pp. 2332–2345, 2005. [10] J.-M. Gorce, M. Arditi, and M. Schneider, “Influence of bubble size distribution on the echogenicity of ultrasound contrast agents—A study of SonoVueTM ,” Invest. Radiol., vol. 35, no. 11, pp. 661–671, 2000. [11] N. de Jong, R. Cornet, and C. T. Lancée, “Higher harmonics of vibrating gas-filled microspheres. Part one: Simulations,” Ultrasonics, vol. 32, no. 6, pp. 447–453, 1994. [12] L. Hoff, Acoustic Characterisation of Contrast Agents for Medical Ultrasound Imaging. 1st ed. Norwell, MA: Kluwer, 2001.

Meng-Xing Tang (M’06) received his B.Eng. degree in biomedical engineering in 1994 and his M.Phil. degree in biomedical imaging in 1997, both from the Fourth Military Medical University, Xi’an, Shaanxi Province, China. He stayed in the same university as an assistant lecturer until 1999, when he moved to the UK to start his Ph.D. study. He completed his Ph.D. degree in 2002 at De Montfort University, Leicester, UK, focusing on image reconstruction of electrical

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impedance tomography applied to early detection of breast cancer. Afterward he joined the Wolfson Medical Vision Laboratory in the Engineering Science Department, University of Oxford, Oxford, UK, as a postdoctoral research assistant in 2002, where he started to work on attenuation correction problems in ultrasound contrast agent imaging. He became a Departmental Lecturer in the same department in 2003. Currently, he is a lecturer in the Department of Bioengineering, Imperial College London, London, UK. Dr. Tang’s main research interests include methods for improved imaging and quantification of local blood flow with ultrasound contrast agent imaging and applications to the diagnosis and treatment of cardiac diseases and cancer. His other interests include nonlinear tomographic imaging and signal and image analysis.

Robert J. Eckersley (M’97) was born in Penzance, UK, in 1970, He graduated from Kings College, London, in 1991 with a B.Sc. degree in physics with medical applications. He completed his Ph.D. degree in 1996 at the Institute of Cancer Research, Sutton, UK, focusing on the potential and limitations of ultrasound imaging for imaging tumor vasculature. Currently he is working as a research associate at Imperial College, London. His interests include the physics of ultrasound microbubble contrast agents, methods for improved quantitation of contrast ultrasound data, novel detection methods, and pulse encoding for contrast imaging.