An experimental method for characterizing microbubbles' oscillations is presented. With a Dual Frequency ultrasound excitation method, both relative and absolute microbubble size variations can be measured. Using the same experimental setup, a simple signal processing step applied to both the amplitude and the frequency modulations yields a two-fold picture of microbubbles' dynamics. In addition, assuming the occurrence of small radial oscillations, the equilibrium radius of the microbubbles can be accurately estimated.
Ultrasonic detection and sizing of microbubbles circulating in blood is of particular interest in the context of divers' desaturation accident prevention. These measurements should be performed in situ by the divers themselves in order to optimize the decompression stages, taking several parameters into account. (1) All microbubbles ranging from 20 to 200 μm circulating in the acoustical measurement zone have to be detected and sized. (2) The measurements have to be performed very quickly (within less than 20 ms) in order to avoid miscounting circulating bubbles. (3) Low acoustical pressures [Mechanical Index (MI) < 0.3] are required to ensure the safety of the measurements, especially at low frequencies (between 10 and 200 kHz).
There exist very few efficient experimental methods of detecting and characterizing microbubbles. In the prevention of decompression sickness, the quantities of micro-emboli present in the blood flow (Eftedal, 2007) are generally assessed by physicians on the basis of the heart sound signals delivered by Doppler systems. Doppler approaches, which can be used only for detection (but not sizing) purposes, often give rise to wrong audio interpretations because of the noise resulting from the cardiac activity. It is necessary to focus on the microbubbles' acoustic characteristics in order to ensure accurate detection and sizing. Other methods involving the use of ultrasound contrast agents (UCA) such as harmonic imaging (Frinking et al., 2000) and sub-harmonic imaging methods (Overvelde et al., 2010) focus on the nonlinearity of the bubbles. But when dealing with natural microbubbles of various sizes, the resonance frequency is not known. Non-linear techniques with which the excitation has to be selected near the resonance frequency and a high MI is required are therefore unsuitable. Bi-frequency methods are also based on the detection of microbubble resonances (Newhouse and Shankar 1984). The latter methods make it possible to detect the presence of microbubbles and calculate their radius. However, none of these methods based on the resonance of the bubbles under investigation entirely meet the requirements: It is impossible to ensure that all the bubbles in the range of radii of interest will be detected within less than 20 ms because the driving frequency needs to exactly match the resonant frequency of the bubble present during this time. In addition, classical transducers are not compatible with the wide range of excitation frequencies corresponding to microbubble radii ranging from 20 to 200 μm (frequencies of about 16 to 160 kHz). Some improvements have been proposed using non-linear excitations (Fouan et al., 2014), but they do not suffice to completely overcome these limitations. In addition, bubbles' radii can be determined with these methods but they yield no information about the microbubbles' dynamic responses.
Optical methods have been presented for measuring microbubbles' responses. In view of the frequencies used in medical ultrasound investigations, only very fast optical cameras would be suitable for this purpose. The idea of probing the bubbles' dynamics was developed at Erasmus MC (Rotterdam, NL) using the Brandaris ultrafast optical camera. In order to improve the UCA detection, the use of an acoustical camera was suggested (Renaud et al., 2012a). The acoustical camera based on the use of bi-frequency methods (Newhouse and Shankar, 1984; Chapelon et al., 1985) is able to measure the changes in the relative radius of a microbubble subjected to an acoustical field (Renaud et al., 2012a). It is therefore possible to identify single bubbles' “buckling state” behavior and nonlinear behavior (Renaud et al., 2014). However, the latter authors (Renaud et al., 2012b) observed that this method has two main limitations: It cannot be used to measure the equilibrium radius or the absolute changes in the bubble radius. The simple approach presented in the present paper may help to provide this complementary information.
The aim of the present study is therefore to produce an acoustical camera for measuring the absolute changes in bubbles' radii. In addition to the amplitude modulation method used by Renaud et al., we also study the information carried by the phase of the HF wave reflected by an oscillating microbubble. By combining these two measurements, it is possible to directly and reliably calculate the equilibrium radius without any need to sweep the whole resonance frequency domain (which can be defined by the full width at half maximum, FWHM).
To deal with the problem of detecting and sizing microbubbles during the decompression phase, the acoustic power transmitted has to be as low as possible in order to prevent newly developing microbubbles cavitating in saturated tissues and the resulting biological damage. In addition, as explained by Renaud et al. (2012a), the amplitude of the probing wave must be low enough to maintain the (quasi-)linear regime. In this set-up, the acoustic pressure of the High Frequency (HF) wave is therefore set at 10 kPa and the acoustic pressure of the Low Frequency (LF) wave is restricted to 5 kPa. The duration of the measurements used for the data acquisition is less than 2 ms, including the 1-ms excitation time. With the “acoustical camera” method, only the variations induced by the LF excitation in the cross-section orthogonal to the direction of propagation of the HF wave are detected. The relative change in the amplitude of the backscattered HF wave (ΔA/A0) can be simply expressed as follows:
where R0 is the equilibrium radius of the bubble and ΔR is the variation of the radius. In the approximation for the radial motion, whenever the wall of the microbubble moves, a Doppler effect will occur and a frequency modulation will be induced. The radial velocity of the bubble's wall (ν) is associated with a shift in the frequency (Δf), and the radius variation ΔR is therefore correlated with both the phase shift Δφ and the incident angle θ of the HF wave, since
2. Experimental tests on the absolute and relative bubble sizing performances
Experiments are performed in a 2 m × 3 m × 0.5 m water tank in order to reduce the effects of any standing waves resulting from the multiple reflections at the boundaries. A hydrojet (Braun OralB) is used to generate microbubbles (with radii ranging from 20 to 200 μm). A thin wire is placed on the path of the rising bubbles, and measurements are performed on a single tethered bubble. Using this simple method, several measurements are carried out under identical conditions and compared. A micro-bubble's radius is assumed to be constant during the 2-ms measurement period (Church, 1988; Fyrillas, 2006). The acoustically characterized bubbles are monitored optically at the same time with a CCD camera. The acoustic measurements are performed using three confocused transducers. The first transducer radiates the LF pumping wave (Ultran, GMP 50 kHz, Hoboken, NJ) and the other two are used for the transmission and reception of the imaging wave (Imasonic, 1 MHz; f = 90 mm, Besançon, France). The two emitting transducers are connected to an arbitrary waveform generator (LeCroy, ArbStudio 1104, four channels, Thousand Oaks, CA). The receiving transducer is connected to a bandpass filter (Krohn-Hite, 3940, dual channel filter, Brockton, MA) and an oscilloscope (Agilent Technologies, Infini-iVision DSO5014A, 100 MHz, Santa Clara, CA). The experimental setup is shown in Fig. 1.
In order to perform both phase and amplitude estimations, as suggested by Renaud et al. (2012a), short sliding time windows are applied to the backscattered HF signals. In each time window, the amplitude of the 1-MHz component is assessed in the frequency domain. At each time-point, the change in the relative radius is determined using Eq. (1). The phase is estimated using the known values of the HF frequency and the angle between the two HF transducers, and ΔR is then calculated using Eq. (3). The time windows must be set between the LF and the HF periods. A 6-μs window duration was adopted for this purpose and a 0.2-μs step is applied between two consecutive windows. These parameters give a final sampling rate of 5 MHz for the measurement of the changes in the bubbles' radius.
For the sake of comparison, two different studies are performed on the two different microbubbles (with radii of 69 and 45 μm) presented in Fig. 2. In Figs. 2(a) and 2(c), the low frequency excitation is a 1-ms chirp with a frequency increasing from 30 to 60 kHz. These frequencies correspond to the resonances of microbubble radii ranging between 50 and 100 μm. In the cases presented in Figs. 2(b) and 2(d), the frequency is constant (60 kHz) and differs from the bubble's resonance frequency (71 kHz). The two excitations are tested on 2 different bubbles, which are measured optically at 69 and 45 μm. Unsurprisingly, the phase modulation recording is noisier than the amplitude modulation recording. This noise level (see the region before and after the excitation in Fig. 2) depends on both the HF and the changes in the bubble amplitude. If these parameters are constant (which was the case in our measurements), the noise level affecting each curve depends on the microbubble's equilibrium radius. The larger the bubble becomes, the greater the absolute variations and hence, the greater the change in the phase will be.
As described above, similar changes in the microbubble's radius are observed with both excitations. In most previous models predicting microbubbles' behavior in response to acoustic excitation, only changes of volume have been taken into account. In other words, the direction of the excitation wave has never been taken into account so far. This is especially true in the case of this method, where the acoustic powers involved are very low (Ainslie and Leighton, 2011). The changes in the radius can therefore be assumed to be equal in both directions. In order to prevent any phase shifts due for example, to the presence of the wire, only the modulus of the change in the radius is assumed to be constant. Under this assumption, it is possible to calculate the equilibrium radius R0 from the amplitude and phase measurements, using Eqs. (1) and (3). For this purpose, the envelopes of both curves are extracted using a Hilbert transform. The ratios between the absolute and relative envelopes observed in the present experiments with both excitations (pulse and sweep) are shown in Fig. 3.
3. Results and discussion
The results presented in Fig. 3 can be interpreted in several ways. The three phases in the excitation scheme are visible. First, when the power is off, the ratio is insignificant because the bubble is not oscillating. Second, when the excitation is applied to the bubble, the ratio becomes almost constant. Last, after the offset of the excitation, the ratio again becomes insignificant. The average ratio during the acoustic excitation time amounted to 67.2 and 39.7 μm with the chirp and burst excitations, respectively. These values are very similar to the equilibrium radii measured with the camera (69 and 45 μm). Unlike the classical Dual Frequency Method, this approach does not require the excitation to encompass the microbubble's resonance frequency. A broadband source covering all the resonance frequencies of the microbubbles present in blood is therefore no longer required. In the case of the present method, one only needs to activate the microbubble in order to detect it and assess the equilibrium radius. The estimation of single microbubbles' equilibrium radii in response to excitations of several kinds is plotted in Fig. 4, which shows that a wide range of radii were obtained.
The values obtained fall very near the first bisector defining the spread between the true (optically measured) and measured absolute radii. It is worth noting that the accuracy depends greatly on the bubble's radius: the larger the bubble, the more accurate the sizing becomes. In particular, a maximum error of 10% was obtained with microbubbles larger than 80 μm. The fact that greater accuracy is achieved with the largest bubbles matches the present needs, since in diver's blood, these bubbles are also the most dangerous ones. There are several possible reasons for the discrepancies observed between the true and measured radii in the case of smaller bubbles. As mentioned above, it is more difficult to detect frequency modulations in small microbubbles. In addition, the impact of the HF wave on the microbubble may become less negligible as we approach the microbubble's resonance domain. However, the most plausible reason may be that the wire starts to have a real impact on the oscillations of smaller microbubbles. When the microbubble is small in comparison with the wire, its size variations may not be the same in all directions. Further measurements using a modified setup (without any wire) would certainly lead to a better understanding of these differences.
The dual modulation method presented in this paper is a considerable improvement in the field of microbubble sizing, since the frequency band of the pumping wave does not have to encompass the resonance frequency of the bubble. Excitations of all kinds which make these bubbles oscillate could presumably be used, especially pulse excitations, which last for a very short time and have a wide frequency range. The results obtained here using an in vitro setup show that a fairly small LF amplitude (<5 kPa) suffices to be able to detect changes in the amplitude and frequency, and hence to accurately determine the equilibrium radius of the microbubble under investigation. Now that the power and duration requirements have been successfully met, we are developing an adapted version of an existing 2-MHz Doppler system with a carefully chosen excitation for in vivo experiments. The last point worth mentioning is that methods based on both frequency and amplitude modulations would certainly shed useful light on the behavior of microbubbles subjected to acoustic excitations. The use of this dual approach would result in a tremendous improvement in the performances of acoustical cameras, since it would provide them with the means of giving quantitative information. This would make it possible to compare the changes of radius occurring in several directions and to study various modes of microbubble vibration using a multi-channel ultrasonic system.
This work was partly supported by the French Research Ministry under the Smart U.S. project, Ref. ANR-10-BLAN-0311, the Provence-Alpes-Côte-D'Azur Council, in the framework of the Comedies project, the Canceropôle PACA and by the French Ministry of Defense under the BORA project.