50 Hz volumetric functional imaging with continuously adjustable depth of focus

Understanding how neural circuits control behavior requires monitoring a large population of neurons with high spatial resolution and volume rate. Here we report an axicon-based Bessel beam module with continuously adjustable depth of focus (CADoF), which turns frame rate into volume rate by extending the excitation focus in axial direction while maintaining high lateral resolutions. Cost-effective and compact, this CADoF Bessel module can be easily integrated into existing two-photon fluorescence microscopes. Simply translating one of the relay lenses along its optical axis enabled continuous adjustment of the focal length. We used this module to simultaneously monitor activity of spinal projection neurons extending over 60 μm depth in larval zebrafish at 50 Hz volume rate with adjustable imaging thickness.


Introduction
Understanding how neural networks integrate inputs and generate outputs is a central goal of neuroscience. Neurons within these networks are distributed in three dimensions (3D). Monitoring their activity dynamics thus requires an imaging modality capable of rapid volumetric rates. Two-photon laser-scanning microscopy (2PLSM), combined with calcium indicators, has become the gold standard tool for in vivo monitoring of neural activity [1][2][3]. Calcium indicators with fast dynamics (rising time of ~40 ms for the dye Cal-520 [4,5] and 80 ms for GCaMP6f [6]) can be used to monitor the firing of individual neurons to understand information flow in a network. However, capturing calcium dynamics of all labeled neurons in a volume within tens of milliseconds is challenging for 2PLSM because it images a volume by serially scanning the excitation focus in 3D.
Recently, we demonstrated a Bessel beam module that turns the frame rate of 2PLSM into volume rate by elongating its excitation focus in the axial direction [7]. The elongated, Bessellike focus allowed us to image calcium dynamics of dendritic spines in 3D in vivo at 30 Hz, an unprecedented combination of high lateral resolution and fast volume rate. In this previous work, we employed a spatial light modulator (SLM) to generate the Bessel focus. Although such an SLM-based Bessel module can flexibly generate Bessel foci with variable lengths, numeric apertures (NA), and engineered axial profiles, it can be a challenge to fit a bulky SLM into existing microscopes with tight space. In contrast, an axicon (conical lens)-based Bessel module, a common method to generate an axially elongated focus, is less expensive and more compact [8][9][10][11][12][13], but can only generate a Bessel focus of a fixed axial length. In real-life neurobiological inquiries, however, it is often desirable to use Bessel foci of different axial lengths to investigate brain volumes of various sizes and/or labeling densities. To generate a Bessel focus with a different length, published axicon-based implementations modified the beam size, employed another axicon, or built an alternative optical path, all of which complicate the design and sacrifice the compactness of the axicon-based system [10,11].
To address these limitations, here we introduce an axicon-based Bessel module with Continuously Adjustable Depth of Focus (CADoF). Simply by translating a lens within this module along its optical axis, we can continuously adjust the axial length of the resulting Bessel focus. We characterized the performance of this flexible module and demonstrated its usability by imaging groups of spinal projection neurons in the midbrain and hindbrain of zebrafish larvae [14][15][16][17][18], and achieved 50 Hz simultaneous volumetric activity imaging of these neurons during escape behavior.

Construction of the axicon-based CADoF Bessel module
The axicon-based CADoF module was built between a Ti-Sapphire laser (Mai Tai HP, Spectra-Physics) and a custom two-photon fluorescence microscope equipped with a resonant galvanometer and controlled by ScanImage2016 (Vidrio Technologies, LLC). The axicon was housed in a lens tube (SM1L05, Thorlabs), which was in turn mounted in a translational cage (CXY1, Thorlabs). The axicon was placed at the front focal plane of a lens (L1 in Fig. 1a) with 80-mm focal length (AC254-080-B-ML, Thorlabs), which transformed the light refracted by the axicon into a ring. An annular aperture mask was placed at the back focal plane of the same lens to spatially filter the ring. A lens pair (L2 and L3 in Fig. 1a, AC254-150-B-ML and AC254-200-B-ML, Thorlabs) relayed the ring onto the galvo scanners and then to the back focal plane of the objective. Both the axicon and the lenses were built within a caged system, allowing easy translation of lens L2 along its optical axis. Two mirrors mounted on rail assemblies (16.011.0130, 16.021.0065 and 16.021.0020, OWIS, Germany) were used to switch between Bessel and Gaussian focus scanning. During system characterization, three convex axicons with apex angle of 178 o were tested. Axicon 1 and Axicon 2 were from the same vendor (1-APX-2-H254-P, ALTECHNA Inc.). Axicon 3 was from ASPHERICON (XFL25-010-U-B).

Design of the annular aperture mask
Annular aperture masks with different annular thicknesses and diameters were designed. Supplementary Code "maskDesign.m" (Matlab) generates four masks with the inner and the outer diameters located at 1/e, 1/(5e), 1/(10e) and 1/(15e) of the peak amplitude of the ring, respectively. The transmittance ratios of these four masks under ideal conditions are 92.4%, 99.0%, 99.6% and 99.8%, respectively (see Supplementary Code "demo1.m").

Zebrafish preparation
All animal experiments were conducted according to the National Institutes of Health guidelines for animal research. Procedures and protocols on zebrafish were approved by the Institutional Animal Care and Use Committee at Janelia Research Campus, Howard Hughes Medical Institute. Larval zebrafish (Danio rerio) of pigment mutant casper [19], which is a compound mutant of mitfa w2/w2 (nacre) and roy a9/a9 , was raised at 28.5 ˚C with a standard procedure [20]. At 5 days post fertilization, 25% w/v solution of Cal520-Dextran conjugate (10,000MW, AAT Bioquest, California) in zebrafish extracellular solution (134 mM NaCl, 2.9 mM KCl, 1.2 mM MgCl 2 , 2.1 mM CaCl 2 , 10 mM HEPES, and 10 mM glucose, adjusted to pH 7.8 with NaOH) was pressure injected into the ventral spinal cord at the level of 20 th myotome segment following standard procedures [21]. The larvae were left in filtered fish system water at 28.5˚C overnight to allow retrograde filling of spinal projection neurons (reticulospinal and vestibulospinal neurons). On the next day, before imaging, larvae were briefly anesthetized by bath application of 0.02% w/v solution of Ethyl 3-aminobenzoate methanesulfonate (Sigma-Aldrich, St. Louis) in filtered fish system water for 1 min. Larvae were mounted dorsal-side up in a small drop of 1.6% low melting point agarose (Invitrogen) on a glass-bottomed dish. The agar covering the caudal body was removed so that the trunk movement could be recorded. Anesthetic was replaced by filtered fish system water. During imaging, the dish containing the fish was tightly glued on the top of a stimulus platform with dental wax (GC Corporation). A loudspeaker (FRS-8, Visaton) was mounted on the platform. Sinusoidal stimulus waveforms (500 Hz, 2 cycles) were generated by a function generator (AFG3102C, Tectronix), amplified by an audio amplifier (LP-2020A, Lepy), and delivered to the loudspeaker. Images were acquired from 2 s before to 5 s after the stimulus with inter-stimulus interval of longer than 1 min. Blood flow and tissue transparency were inspected after the imaging experiments to confirm that two-photon excitation beam did not damage the brain tissue.

Data analysis
All functional images were registered using an iterative cross-correlation-based registration algorithm [22]. ROIs were manually outlined and then compared with Gaussian 3D image stack for the anatomy. For the calculation of the calcium transient F/F, each ROI across different trials shared the same baseline, determined as the mean calcium fluorescence signal in the 1sec window prior to the stimulus. Those trials that had spontaneous calcium transients within this pre-stimulus window were excluded from baseline calculation. A neuron was defined as responsive if the amplitude of the maximal calcium transient was bigger than the mean + 3SD of the baseline. Scan time lag resulting from different cell positions and the vertical scanning of y galvo was corrected according to vertical positions of centroids of individual ROIs.

Axicon-based CADoF module
To generate continuously adjustable Bessel foci, we started with the optical path similar to conventional axicon-based Bessel beam module [10,11]. Placed between the light source and the microscope (Fig. 1a), the key component of the module is an axicon. The axicon has a conical surface, where light is refracted according to Snell's law. The lens L1 then shapes the light into a ring at its back focal plane, which is in turn projected by a lens pair consisting of L2 and L3 to the galvo scanning mirrors, and then to the back focal plane of the objective by another lens pair L4 and L5. The annular aperture mask placed at the back focal plane of L1 is optional, but helps to shape the axial profile of the two-photon excitation point spread function (PSF) by blocking the unwanted light that arises from the imperfections of the axicon. This optical design is conceptually similar to the traditional axicon-based modules [10,11,23]. The novelty of the present study, however, is that by moving the lens L2 along its optical axis, we can continuously vary the axial length of the Bessel focus ( Fig. 1 and Visualization 1).
(Moving lens L3 also varies the axial length -for simplicity, we only discuss the effects of translating L2.) Fig. 1b shows three representative (long, medium, and short) axial PSFs with full-widths-at-half-maxima (FWHMs) of 39 µm, 24 µm, and 14 µm at lens L2 displacements of D=-12 mm, 0 mm, and 12 mm, respectively. When the displacement of L2 is negative (i.e., moving L2 closer to the mask), more power is allocated to the central region of the objective back focal plane (Fig.2, 1st column), which yields a smaller effective NA and, together with the phase distribution of the pupil function, a longer Bessel focus. In contrast, moving the lens  away from the mask distributes more power to the edge of the objective pupil function, leading to a bigger effective NA and a shorter focus (Fig.2, 3rd column). This way, moving the lens from left to right in Fig. 1a allows us to continuously change the lateral and axial FWHMs (Figs. 1c, d). Numeric simulations using the vector diffraction theory developed by Richards and Wolf [24] agree well with the experimental data (Figs. 1c-f), where the difference between the lateral resolutions along x and y axes is caused by the linear polarization of the excitation light (Fig. 1c). It is worth noting that there is a tradeoff between axial/lateral FWHM and the peak signal. Given the same power at the axicon, longer Bessel foci (negative D values in Fig.  1d) have larger lateral FWHMs (Fig. 1c) and smaller peak signals (Fig. 1e), because there is less energy in the central peak of the foci. For the shortest Bessel foci, light starts to be clipped by the objective, leading to a decrease in the post-objective power (Fig. 1f). Fig. 1 was achieved by having a thin annular aperture mask (e.g., 52 m thickness used for data in Fig. 1) to correct for the imperfections of the axicon (Fig. 3) [13]. However, such a thin mask causes power loss (Fig. 3), which might become problematic in systems with limited excitation power. One can use a thicker mask or even operate without mask and obtain non-theoretical yet still desirable axial profiles. Another method to alleviate the deviation from theoretical predictions is to substantially expand the beam before the axicon [25,26]. To maintain the compactness of the module, we did not adopt this strategy.

Axicon-based CADoF module enables flexible control over interrogated volume thickness in zebrafish larvae
To demonstrate the flexibility of the CADoF module, we first imaged groups of spinal projection neurons (reticulospinal and vestibulospinal neurons) in the midbrain and hindbrain of larval zebrafish. These neurons form a stereotypic organization arranged in a volume around 400 m × 200 m × 100 m (rostrocaudal, mediolateral, and dorsoventral axes, respectively) and were retrogradely labeled with fluorescent tracer dye injected into the spinal cord, permitting easy identification of individual neurons from one zebrafish to another [18,27]. Here we defined the origin of relative depth (z = 0 m, 96 m from the skin surface) as the plane where the first labeled structure appeared when the objective was moved from the dorsal to ventral part of the zebrafish. Scanning a Gaussian focus (axial FWHM: 2.6 m) in 2D, we could only image a subset of neurons (e. g., at maximum, 38 neurons, Fig. 4a). To sample the 74m-thick volume containing all labeled neurons, 28 slices of 2D images have to be sequentially acquired (Fig. 4b). With the CADoF modality, even the shortest Bessel focus revealed more neurons without moving objective (arrowheads in Fig. 4c). As the Bessel focus continued to extend axially, more cells showed up successively (arrowheads in Figs. 4d-j). The longest Bessel focus revealed 108 neurons (Fig. 4j), with a lateral resolution that provided comparable cellular-resolving power to the mean-intensity projection image of the 2D Gaussian image stack along the dorsoventral axis (Fig. 4b).

50 Hz volumetric calcium imaging of spinal projection neurons in zebrafish larvae.
After demonstrating the performance and flexibility of our axicon-based CADoF Bessel module on structural imaging of the spinal projection neurons, we moved on to investigate the activity dynamics of these neurons in zebrafish larvae engaging in escape behaviors [14][15][16][17]. We retrogradely labeled these neurons with a calcium indicator dye (Cal-520 dextran) from the ventral spinal cord. Acoustomechanical tapping stimuli were applied during imaging to trigger escape response and neural activity (Visualization 2). In one zebrafish (Fig. 5), the labeled neurons were distributed in a volume of 366 m × 214 m × 66 m (Visualization 3). Gaussian focus scanning over a single plane (Fig. 5a) revealed four active neurons (regions of interest, ROIs 1-4, Fig. 5b) including two Mauthner cells (ROIs 1 and 2, the largest bilateral pair of reticulospinal neurons known to initiate escape behaviors [28][29][30]) as reported in a previous study [31]. Switching to the CADoF module used in Fig. 4, we measured calcium activity from neurons distributed in volumes of varying thickness at 50 Hz volumetric rate. The short Bessel focus (14 m axial FWHM, D = 12 mm, Fig. 5c) revealed the same four active neurons (Fig.  5d) with similar responses to those observed with Gaussian focus scanning. The medium Bessel focus (24 m axial FWHM, D = 0 mm) uncovered six additional responsive neurons (ROIs 5-10 in Figs. 5e,f). Scanning the long Bessel focus (39 m axial FWHM, D = -12 mm) covered the entire 366 m × 214 m × 66 m volume and further revealed another five active neurons (ROIs 11-15 in Figs. 5g,h). In addition, the calcium transient signal-to-noises of several neurons increases by having a longer Bessel focus integrate the signal throughout their cell bodies (ROIs 3,5 and 9). Overall, for the 36 neurons that were labeled by Cal520 dextran in this fish (Figs. 5i,j), we monitored their activity at 50 Hz and identified 15 neurons that exhibited tapping-evoked calcium transients.

Discussions
Bessel focus scanning for volumetric imaging provides several advantages: reduction of data size, resistance to artifacts induced by axial motions, compatibility with other volumetric imaging method [32], and easy integration into existing microscopes as a standalone module [7]. In practice, it is desirable to have the length of Bessel focus continuously adjustable: For samples with sparse labeling, a long (e.g., > 100 m) Bessel focus can monitor activity over a larger volume. For more densely labelled samples, a shorter Bessel focus (e.g., 30 to 80 m) can reduce the occurrences of overlapping structures. An even shorter (e.g., 20 m) Bessel focus is sufficient when used to eliminate axial-motion-induced image artifacts during experiments with behaving animals. Both SLM-based [7] and axicon-based CADoF (Fig. 1) Bessel modules can generate Bessel foci of continuously tunable axial lengths. SLM-based Bessel beam module achieves this by varying the phase pattern loaded on the SLM [7]. Here, we showed that displacing the Lens L2 in Fig. 1 in the axicon-based CADoF Bessel module changed the electric field distribution at the objective back focal plane (Fig. 2), where variations in both the amplitude and the phase of the electric field work concertedly to generate Bessel foci of different axial and lateral widths. (If we maintain the amplitude distribution but force the phase of the electrical field on the back pupil plane to be constant, the resulting pupil function fails to produce a Bessel focus, Visualization 4). Although the module described in this paper does not have the same flexibility in engineering the PSF profiles as SLM-based modules do [7,33], this axicon-based Bessel module costs much less to set up (~$5,000, rather than $30,000, for the entire module), occupies less space (due to its transmissive layout), and is insensitive to polarization of the light, making it an attractive alternative to the more expensive modules.
We used the axicon-based CADoF Bessel module for 50 Hz volumetric calcium imaging of spinal projection neurons in zebrafish larvae during behavior (Figs. 4, 5). Because more energy is distributed in the side rings of the Bessel foci, to get the same signal, higher average power is required for Bessel foci than for Gaussian ones. We did not observe damages on brain tissue, even after dozens of imaging trials. This may be attributed to two factors: the amount of two-photon excitation, as reflected by the final fluorescence signal, stayed similar, indicating that Bessel focus scanning does not introduce additional photo-excitation-related damages; the absorption of the 940 nm light by the larval brain and the immersion media was minimal, thus leading to minimal heating-related damages.
The ability to measure the activity of all neurons within the image volume simultaneously using the axicon-based CADoF Bessel module, instead of plane by plane as done in conventional approaches, would make it possible to study the neural correlates of complex behavior repertoire in single trials. For sensors of neural activity [34] (e.g., for neurotransmitter release or membrane voltage) whose transients are much shorter in time than calcium sensors, the ability to image a volume at tens of Hz as we demonstrated here would be essential to capture all the activity events during behavior. For targeting neurons within smaller fields of view, one can image at even faster volume rate by reducing number of scanning lines. Beyond neural imaging, this axicon-based CADoF Bessel module can benefit other applications where an extended focus is used for optical measurement or manipulation.