# Spatial ultrasound modulation by digitally controlling microbubble arrays

Sep 10, 2020

### Principle of spatial ultrasound modulation via a microbubble array

Implementing a dynamically reprogrammable phase plate similar to the static acoustic hologram8 is an engineering challenge. The obvious approach through, e.g., deformable surfaces30,31, requires the integration of many actuators with spacing and displacements at the ultrasound wavelength scale. Alternatively, controlling dispersion could efficiently modulate the phase of an ultrasound wave, but no suitable material or meta-material concept has been found to date. Amplitude modulation promises a more viable solution instead of phase29. Though a binary amplitude hologram contains only two states for each element, which decreases its information capacity compared to multiple-level phase modulation, it could still afford complex image generation, simply by providing many more elements in total29.

Due to the significant acoustic impedance mismatch between gas and liquid, a thin layer of air in liquid can effectively stop ultrasound, even when its thickness is less than the acoustic wavelength. A microbubble can thus serve as a local sound blocker. A pattern of microbubbles in the path of an ultrasound wave should, therefore, impart a corresponding amplitude pattern onto the wavefront of the acoustic field, which is the operating principle of our SUM, as shown in Fig. 1a. Patterning a large number of microbubbles enables the on-demand shaping of an acoustic field’s amplitude distribution (Fig. 1b). Moreover, the dynamic control of the microbubble pattern enables dynamic spatial acoustic modulation. Based on this concept, our dynamic spatial ultrasound modulator (SUM) generates reconfigurable microbubble patterns.

For example, even a 20-μm gas layer leads to a negligibly small transmission coefficient (on the order of 10−7), considering a 10-MHz acoustic wave (wavelength 150 µm). This can be seen from the power transmission coefficient for an acoustic wave at normal incidence through a plain layer32:

$$C_T = frac{1}{{xi ^2sin ^2left( {k_Ldelta } right) + 1}},$$

(1)

$$xi = frac{1}{2}left| {frac{{Z_L}}{{Z_M}} – frac{{Z_M}}{{Z_L}}} right| = frac{1}{2}left| {frac{{rho _Lc_L}}{{rho _Mc_M}} – frac{{rho _Mc_M}}{{rho _Lc_L}}} right|,$$

(2)

where δ and kL are the layer thickness and wavenumber in the layer material, respectively; Z, ρ, and c are acoustic impedance, density, and speed of sound, respectively; the subscripts L and M indicate the layer and the surrounding host medium. The sound speed in water (ρM ~ 1000 kg m−3) is cM ~ 1500 m s−1 and in air cL ~ 343 m s−1 at atmospheric pressure (ρL ~ 1.23 kg m−3). As the ratio of acoustic impedances increases, the wave is increasingly reflected at the interface, and therefore, less energy is transmitted through the layer. Since air blocks ultrasound so well, we now need to find a way to generate programmable on-demand microbubble patterns.

Our SUM device architecture consists of a CMOS chip placed on top of an acoustic transducer, as shown in Fig. 2. A liquid film of electrolyte is sandwiched between the chip surface and a conveyor film. The CMOS chip surface has 10,000 individually addressable electrodes (70 μm by 70 μm gold pads in a 100 µm by 100-µm raster). Positioned next to the chip is a copper electrode, which serves as the anode. A switchable DC power supply provides a potential difference between the copper electrode (+5 V) and the 10,000 gold electrode pads of the CMOS chip. Once the DC power is switched to a CMOS pixel, the electrolysis of the surrounding water solution generates hydrogen and oxygen gas, respectively, at the gold and copper electrodes. As we will see below, the current is controlled to define the size of the microbubbles.

To generate a target acoustic field, we first compute a binary amplitude hologram8, which is a binary transmission function that can be directly translated into a pattern of microbubbles. The CMOS chip then generates microbubbles according to this pattern. Each microbubble corresponds to a location of zero ultrasound transmission (Fig. 2a). After the bubble generation is completed, the transducer is turned on (Fig. 2b), and the acoustic wave transmits through the SUM and is locally blocked at the pixels that are covered by a microbubble. The remainder of the wavefront propagates into the upper container and diffracts to form the target sound pressure distribution. To visualize the pressure field at the target plane, we introduced submillimeter PDMS particles suspended in water, which then assemble into the shape of the projected sound pressure image. To conclude the sequence and prepare the SUM for the next frame, the microbubbles are cleared by horizontally translating a conveyor film (Fig. 2c), which drags the bubbles out of the device. The complete modulation process is shown in the Supplementary Movie 1.

### Microbubble generation

The SUM generates a pattern of microbubbles on the surface of the CMOS chip by the electrolysis of water. The microbubble coverage has to be large enough to ensure that the acoustic wave is blocked at the location of the electrode. As the potential difference between the anode and the cathode is constant (5 V), the microbubble volume depends on the time the current flows. The size of the microbubbles as a function of the time of the electrolysis (0.6, 0.8, 1.6, 2.4, and 2.8 ms) is shown in Fig. 3. The area (XY plane) covered by microbubbles increases with the duration of the electrolysis. An adequate microbubble volume also ensures that the bubble is trapped between the conveyer film and the chip surface. The adherence to the solid surfaces appears quite strong and retains the microbubbles against buoyancy even when the device is turned to a vertical orientation33. This suggests that the operability of our SUM is independent of its orientation, as shown in Supplementary Fig. 1. However, as the microbubbles grow, neighboring bubbles can fuse, which is shown in Fig. 3g. This distorts the microbubble pattern because the resulting merged bubbles adopt a spherical shape due to surface tension. We empirically determined that a flow of current between 1.6 and 2.4 ms, marked in blue in Fig. 3g, maximizes the bubble coverage while keeping the fusion of bubbles low.

Figure 3h shows the simulated relative acoustic transmission coefficient for different bubble coverages across a single pixel. The relative acoustic transmission coefficient is the ratio of the acoustic intensity transmitted through a bubble covered pixel versus an uncovered pixel. It can be seen how the selected bubble coverage (marked blue), resulting from the selected electrolysis time, effectively blocks 99% of the incident acoustic intensity. It should be noted that the applied acoustic frequency (10 MHz) is far above the fundamental resonant frequency (on the order of 100 kHz) for 10-μm-sized microbubbles in water34. Thus, the bubble vibration excited by the incident acoustic waves is negligible35. Accordingly, we do not observe bubble motion even when the intensity at the transducer reaches about 5 W cm−2, which is sufficiently high for microparticle assembly and manipulation.

### Binary amplitude acoustic hologram

For each acoustic image, the microbubble pattern is pre-calculated as a binary amplitude acoustic hologram, consisting of pixels with an amplitude of zero or one. Similar to a phase hologram (Fig. 4a, d)8, the binary amplitude hologram (Fig. 4b, e) can also be optimized using the iterative angular spectrum approach (IASA). In this special case, however, the phase distribution in the hologram plane is at each step converted to a binary amplitude distribution with a fixed phase. An average phase value is obtained from the back-propagated target image. The hologram pixels, whose original phase is within the range of ±π/2 from this average value, are set to an amplitude of one, and the remaining pixels are set to zero. The algorithm typically converges in <30 iterations.

Figure 4 shows simulations of reconstructed sound fields, and their corresponding holograms for a phase hologram (panels a, d) and binary amplitude hologram (b, e) encoding the letter “R”. Since the pixels in binary amplitude holography only have two states (Fig. 4e), they naturally provide much less information density than phase holograms which provide almost a continuous modulation over a range of 2π (Fig. 4d). This results in an elevated background noise that can be seen when comparing Fig. 4b with 4a. On the SUM chip surface, microbubbles replicate the zero-amplitude pixel pattern designed by the binary amplitude holography (Fig. 4f). The 10-MHz transducer emits an acoustic plane wave that transmits through the chip layer and then reaches the microbubble layer. The wave is blocked by each bubble and therefore modulated in amplitude. Where there is no microbubble, the wave transmits and diffracts to form the calculated acoustic image in the target plane (Fig. 4c). To demonstrate that the SUM can be used to project changing acoustic fields, we show a movie of the corresponding hydrophone scans in the Supplementary Movie 2. In this video, each frame was formed in 15 s, and the resulting field was raster-scanned by a needle hydrophone before clearing the bubble pattern and creating the next frame.

### Dynamic microparticle manipulation based on SUM

Acoustic particle manipulation is an emerging technique with promising applications in fabrication36 and biomedical engineering18. To date, however, methods for dynamic and parallel manipulation have been limited to few particles25 or highly symmetric arrangements37. As shown in Fig. 5, the present SUM is capable of dynamically assembling microparticles into arbitrary target patterns. We use PDMS particles, which have a positive acoustic contrast in water. Thus, the acoustic radiation force on these particles will push them toward areas of high acoustic amplitudes. For each acoustic image, it takes around 12 s to write the microbubble hologram, when each pixel is sequentially addressed. Afterward, the transducer is turned on for 15 s, generating ultrasound waves, which are modulated by the SUM and propagate to form the acoustic image in the target plane, where the PDMS particles aggregate into the corresponding shape. After each assembly step, the transducer is turned off, and a motorized film mechanically “wipes” the microbubbles off the chip surface. In one experiment, the sequence of microbubble writing, particle assembly and bubble removal is repeated seven times to sequentially assembly the particles in the shape of the letters “A” to “G”. A video of this dynamic microparticle manipulation is shown in Supplementary Movie 3.