Light sheet microscopy with acoustic sample confinement

Contactless sample confinement would enable a whole host of new studies in developmental biology and neuroscience, in particular, when combined with long-term, wide-field optical imaging. To achieve this goal, we demonstrate a contactless acoustic gradient force trap for sample confinement in light sheet microscopy. Our approach allows the integration of real-time environmentally controlled experiments with wide-field low photo-toxic imaging, which we demonstrate on a variety of marine animal embryos and larvae. To illustrate the key advantages of our approach, we provide quantitative data for the dynamic response of the heartbeat of zebrafish larvae to verapamil and norepinephrine, which are known to affect cardiovascular function. Optical flow analysis allows us to explore the cardiac cycle of the zebrafish and determine the changes in contractile volume within the heart. Overcoming the restrictions of sample immobilisation and mounting can open up a broad range of studies, with real-time drug-based assays and biomechanical analyses.


Supplementary Note 1: Diffusion speed of fluorescein in water and agarose
The speed of molecular diffusion depends on parameters such as temperature, viscosity of the fluid and the mass of the compound. To demonstrate the different diffusion speeds of a compound in water and agarose, we investigated fluorescein's diffusion process since its concentration can be easily quantified with the fluorescent signal intensity.
First, we tested the delivery of fluorescein solution into the sample chamber with our circulation system. To be more specific, purified water was circulated in the sample chamber and a beaker with PVC tubing, with the total volume of water to be 200ml. Before the start of the measurement, the peristaltic pump was stopped, then 2ml of 0.1 mM fluorescein was added into the beaker. The 488nm laser was delivered to the center of the sample chamber, and the fluorescent signal of fluorescein was collected with the existing LSFM, at the same time as the pump was started. Since the intensity of the signal is linearly proportional to the concentration of fluorescein, this serves well for quantifying the relative concentration of fluorescein at the imaging point. The fluorescent signal was recorded every 2 seconds for 30 minutes.
This was repeated with an agarose cylinder suspended in the center of the sample chamber. The illumination laser was delivered to the center of the agarose rod whilst the fluorescent signal was recorded. All the other conditions were the same. The test was repeated with 1mm diameter and 2mm diameter agarose rods.
Fluorescent intensity integrated across the whole frame is plotted below: Without agarose, it took less than 1 minute for the compound to reach the imaging area. Then the concentration of the compound reached the top at around three minutes. Whilst in agarose, the diffusion is much slower. After 30 minutes, the fluorescein concentration in agarose is only approximately a quarter of that in water.

Supplementary Note 2: Supplemental drug study utilizing this system
Additional experiments were carried out on older 3-dpf zebrafish to validate the effect of age on heart rate increase. Supplementary Figure 2 shows a significantly higher response to norepinephrine than observed in 2-dpf zebrafish, shown in the main text. Developmental age has profound influence on the capacity of the cardiovascular system to respond to drugs 1 , which is reflected here. The mean increase of approximately 17% is consistent with the previous literature 2 .
Supplementary Figure 2: Normalised heart rate in 3 days-past-fertilisation zebrafish with the addition of 1 mM of norepinephrine. No drug was added in period (i) for 30 minutes, drug was added in period (ii), and washed out in period (iii). The plot is presented as a mean value (solid lines) with error bounds of one standard deviation (dashed lines) across all results (dotted lines; n=2).
In addition to the focused drug treatment described in the main text of our paper, further tests were conducted with older zebrafish larvae, as shown in Supplementary Figure 3. Verapamil and high-dose tricaine were given, respectively, to 5-day-old and 4-day-old zebrafish, following the same procedure as in the manuscript.
Due to the greater age of these zebrafish, their transparency was reduced, leading to reduced image quality. Nevertheless, we were able to extract the heart rate via video analysis.

Supplementary Note 3: Optical performance of the ETL
The electrically tunable lens (ETL) is a liquid lens that provides tunability over a focal power range from 5 dioptres (200 mm) to 10 dioptres (100 mm). This focal power range is offset by -10 dioptres via addition of a concave lens with f = -100 mm at the back of ETL. The position of the image plane is changed by applying a current to the ETL, ranging from 0 to 292 mA. With the present arrangement, an infinite focus of the ETL was achieved with a driving current 220mA. For most of our work, the ETL was driven with a triangular waveform, providing a range from 170 to 270mA.

Scanning depth range
The scan depth of the ETL was calibrated using a low frequency (10 Hz) drive waveform. The measurement was performed by manually translating a fluorescent bead along the detection axis and monitoring the range over which the bead appeared / disappeared from view. In the arrangement shown in Supplementary Figure 6a, the manual stage provided translation along a direction that is diagonally disposed with respect to the detection path, which just introduces a factor of √2 into the calibration. Upon repeating the above procedure six times and averaging the results, we obtained the scan range of the ETL driven at 170 to 270mA as 249.6 ± 3.0 μm. This range can be extended by driving the ETL with a larger amplitude waveform.

Optical resolution
The ETL is meant to reside in the back focal plane of the objective lens, which could be achieved via projection optics. However, in our compact setup, we simply place the ETL directly after the objective, where it is oriented at 45° with respect to vertical. As the ETL membrane is elastic, the lens shape is influenced by gravity. Such issues demand that optical resolution be experimentally assessed for this arrangement. With a detection NA of 0.5 and the spectrum of the fluorescent signal centred on 0.6 μm, the diffraction-limited resolution (0.61λ / NA) is 0.73 μm. Without the ETL, the estimated resolution (based on FWHM of fitted Gaussian curve) is 0.84 μm (Supplementary Figure 4 (a)), which is slightly worse than the diffraction limit, potentially because the tube lens we used is not the optimal lens for the Olympus objective.
With the ETL introduced into the setup, optical resolution on three planes was examined, with a driving current on the ELT, Supplementary Figure 4(b) 170mA, (c) 220 mA and (d) 270 mA respectively. It can be seen that with the presence of the ETL, the contrast and resolution of the image are slightly affected, potentially because of the sub-optimal orientation of the ETL.
With the ETL, we can still achieve submicron resolution.
To eliminate the effect of gravity, we have suggested an alternative optical setup, featuring dual-side illumination and a horizontally arranged ETL. Details are given in Supplementary Note 4: Alternative optical setup.

Actual magnification
Having the ETL directly after the objective, in contrast to a 4f system, leads to a change in the FOV when changing the focal length of the ETL 3 . We measured the resulting FOV by translating a reference target (a fluorescent bead) across the entire FOV and recording the reading on a manual actuator. This process was repeated three times and averaged to obtain the FOV, then repeated in three planes, i.e. ETL driven at 170 mA, 220 mA and 270 mA statically. The results are as follows: Supplementary We found that within this scanning range, the actual magnification difference is within ±6% and considered negligible. If necessary, this effect could be avoided by adding a 4f-system in the detection arm and placing the ETL between the two lenses of this system.

Supplementary Note 4: Alternative optical setup
Here we discuss the potential merits of an alternative arrangement, shown in Supplementary Figure 5. This setup utilizes both sides of a horizontally oriented breadboard, with illumination path and sample chamber above the breadboard, while detection optics and the camera reside beneath the breadboard. This arrangement has several advantages: 1. This orientation of the ETL will minimize wavefront error due to the influence of gravity. 2. Specimen loading is simplified in this geometry: an acoustically trapped sample will automatically be in focus optically. 3. Dual-side illumination helps to improve image quality. Otherwise, there is no fundamental difference between this arrangement and our current setup, so we believe such a conversion to be straightforward.
Supplementary Figure 5: Alternative optical arrangement, featuring dual-side illumination, optimized orientation for ETL, and simplified sample loading. Again, a laser beam is expanded such that a light sheet is formed on a scanning mirror. Here, though, after going through a relay lens pair, the beam is split into two by a 50:50 beam splitter. The relay lenses on two arms have the same ratio, so the result scanning light sheets coincide in the sample chamber. This compact setup only occupies a space of 50 × 50 × 20 cm 3 . The second channel of the function generator outputs a sinusoid at the resonant frequency of the ultrasonic transducers, which is amplified to the required levels by a bespoke RF power amplifier.

Supplementary Note 5: Experimental setup
Additional hardware includes a peristaltic pump (MINIPULS 3, Gilson) used to circulate fluid in the sample chamber and a laser shutter. Both the pump and the laser shutter were controlled remotely, via serial port communication with an Arduino board.

Supplementary Note 7: Ultrasonic transducer / resonant device design and modeling
To design the ultrasonic force control system, a spherically concave, single-element transducer and a pair of confocal transducers were modeled using a finite-element analysis (FEA) package (PZFlex Ltd, Glasgow, UK), allowing comparison of predicted behavior and experimental performance.
Supplementary The symmetry of the experimental system suggested the use of two-dimensional (2D) axisymmetric computational models, for which we input the material properties listed in Supplementary Tables 2 and 3. In the PZFlex modeling environment, any given piezoelectric material can be assigned only one unique poling direction, and so our model of a radially poled, spherically concave single-element PZ26 transducer was divided into 88 arc sections, each subtending an angle of 0.879°, with individual poling directions directed towards the focal point. The FEA mesh size was 40 × 40 µm 2 , which is approximately 4% of the wavelength in water at 1.5 MHz, providing a high degree of confidence in the results. In both models, the column of air behind the PZ26 components was represented as a free boundary condition assigned at the maximum of the x-axis. For the confocal device model, a symmetrical boundary condition was assigned at the minimum of the x-axis. An absorbing boundary condition was assigned at the other limits of the x-axis and at both limits of the y-axis for both models.
The single-element model was excited with a one-cycle sinusoid at 1.5 MHz and the simulation was allowed to run until oscillation decayed to 10% of its maximum. The model confocal system was excited with the same signal but runtime was adjusted to allow the ultrasonic pulse to complete eight one-way trips between the two transducers.
Supplementary Electrical impedance spectra for each model were derived from the simulated voltage and current responses. Supplementary Figure 8 compares these simulated electrical impedance spectra with our experimentally measured results for one device geometry. The relatively good agreement was taken to support the use of such simulations for device design.
Supplementary Figure 9 shows our simulated results for a focused ultrasound beam from the single-element transducer at f = 1.468 MHz, given an excitation amplitude of 1 Vpeak. For the confocal system model, the pressure responses were recorded in the time domain at the geometric center of the water and at a point 1.2 µm away from the center on the x-axis. After performing a fast Fourier transform on the time-domain response and normalizing for the input voltage, the pressure response spectra were extracted as shown in Supplementary  Figure 10. Because of the resonant nature of the system, the periodic system resonances vary compared with those of the ultrasonic transducers. As can be seen in Supplementary Figure  10, the resonances of the confocal system are superposed on the resonant behavior of the single element transducer. Additionally, the frequency of the maximum pressure response in the confocal system, f = 1.519 MHz, is distinct from the resonant frequency of the singleelement transducer.
The periodic system resonances shown are dependent upon the low level damping assumed for the resonance device and this is also linked to the fact that the wavelength of ultrasound in water is much less than the thickness of the water layer 4 . The resonant frequency of the transducer and the system resonant frequencies with peak pressure responses were selected to observe pressure distributions. Supplementary Figure 11(a) and (b) show the normalized ultrasound pressure fields of the confocal system driven at f = 1.468 MHz and f = 1.519 MHz, respectively. Significantly, the maximum pressure amplitude at f = 1.519 MHz is more than three times that at f = 1.468 MHz.
Supplementary Figure 8: PZFlex simulated electrical impedance spectra of the spherically concave, single-element transducer compared with experimental measurement