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Quasi-simultaneous multiplane calcium imaging of neuronal circuits

Two-photon excitation fluorescence microscopy is widely used to study the activity of neuronal circuits. However, the fast imaging is typically constrained to a single lateral plane for a standard microscope design. Given that cortical neuronal networks in a mouse brain are complex three-dimensional structures organised in six histologically defined layers which extend over many hundreds of micrometres, there is a strong demand for microscope systems that can record neuronal signalling in volumes. Henceforth, we developed a quasi-simultaneous multiplane imaging technique combining an acousto-optic deflector and static remote focusing to provide fast imaging of neurons from different axial positions inside the cortical layers without the need for mechanical disturbance of either the objective lens or the specimen. The hardware and the software are easily adaptable to existing two-photon microscopes. Here, we demonstrated that our imaging method can record, at high speed and high image contrast, the calcium dynamics of neurons in two different imaging planes separated axially with the in-focus and the refocused planes 120 µm and 250 µm below the brain surface respectively.


Introduction
With the advancement of ultrafast laser technology, two-photon excitation fluorescence (2PEF) microscopy is becoming a common imaging tool in life science research. In particular, 2PEF microscopy is well suited for studying the neuronal activity in awake, behaving animal models. Cortical circuits process information in a highly distributed, parallel manner in three-dimensional (3D) space distributed over six anatomically distinct layers. Precisely how neural activity in these different layers enables information processing remains a key question in the field of neuroscience. Neural network models highlight the importance of quantitative understanding of the relationship between the activities in the input and the output layers on a trial-to-trial, rather than on an averaged basis [1,2]. In view of that, various techniques have been developed to enable fast 3D scanning in multiphoton microscopy. For example, several groups have developed versatile 3D random excitation for functional neural imaging with ultrafast acquisition rate based on the free beam steering capability afforded by pairing acousto-optic deflectors (AODs) [3][4][5]. Electrically tunable lens (ETL) is another useful device to aid the axial optical scanning without direct mechanical interference on the specimen. Because of the ease of use, ETL appeals to many scientists in developing new imaging techniques. Its applications cover not only the widefield and the confocal microscopy fronts [6,7] but also extend further to enhance multiphoton imaging techniques enabling the rapid excitation within volumes [8][9][10][11]. The remote focusing technique can assist high axial scan rates in a high numerical aperture (NA) condition without introducing aberrations [12-at the focus is crucial for the non-linear fluorescence excitation; (2) mechanical agitation of the specimen must be avoided. Apart from that, wavefront shaping devices such as spatial light modulators (SLM) and deformable mirrors (DM) have played important roles in brain imaging. For instance, their applications can be found not only in the aberration correction for in vivo imaging [15,16] but also in the multi-site targeted excitation of neurons [17,18] and the rapid spatiotemporal remote focusing [19]. Also, in conjunction with the DM based axial refocusing, concurrent multifocal detection can be realised through multiplexing the laser pulse train [20,21]. Similar time multiplexing via pulse delay but with added spatial beam separation through multiple beamsplitters has been reported to enable simultaneous multiplane 2P calcium imaging [22]. While the aforementioned techniques have various technical merits, their complexity hampers easy incorporation into existing multiphoton microscopy systems.
In order to capture the fluorescence of genetically encoded calcium indicators GCaMP [23] from axially separated neurons, we set out to develop an imaging technique that overcomes the slow axial scanning in a standard multiphoton microscope while retaining the planar image quality at minimal cost. This was achieved based on the idea of creating instantaneous optical switching of the laser propagation towards different beam pathways constructed with and without the remote focusing system. Thus, an AOD was integrated into the multiphoton microscopy system to obtain fast, inertia-free optical path switching. This permitted beam steering within microseconds to access different optical pathways that were configured to refocus the beam. One beam path entered the microscope in the conventional manner, whereas the other beam path passed through a remote focusing system that could translate the focal plane by up to few hundreds of micrometres away from the nominal focal plane. In attaining a high NA refocusing over an extended volume for an existing commercial microscope, we adopted the remote focusing technique by incorporating a pair of high NA lenses outside the microscope body with one lens allowed to translate in the z direction. This technique allows the axial translation of the focal spot along the optical axis without introducing substantial aberrations and circumvents the mechanical interference on both the animal specimen and the focusing objective lens. Integration of both the AOD switching and the remote focusing techniques can be easily implemented to convert a standard single plane scanning microscope into a fast switching multiplane microscopy system for studying stimulated responses in a 3D neuronal circuit at a fraction of the cost of more complex multiplane imaging methods.
Here, we characterised the performance of this system using a 3D bead sample and demonstrated its application through multiplane recording of neocortical circuit activity with neurons expressing GCaMP6s.

Design principles and validation
2.1 Quasi-simultaneous multiplane imaging system design 2.1.1 Acousto-optic deflector for fast switching and its dispersion compensation An AOD affords a motion-free laser beam steering capability. However, the diffractive nature of the tellurium dioxide (TeO 2 ) crystal that constitutes the main driving component of the AOD is wavelength sensitive. Depending on the spectral bandwidth of the laser source used, the beam may experience appreciable spatial and temporal dispersion propagating through the AOD. In most cases in multiphoton microscopy, where a Ti:Sapphire ultrafast laser with the spectral bandwidth of ~10 nm is the preferred excitation source, the beam will be stretched spatio-temporally by the AOD leading to a significant reduction in the 2P excitation power and adverse distortion in the acquired fluorescence images. Therefore, pre-compensation for the AOD spatio-temporal dispersion has to be taken into account. Here, we used a SF11 equilateral dispersive prism (PS859, Thorlabs, USA) to recover the initial laser beam shape and its pulse duration [24][25][26][27]. Because the AOD functions as the fast horizontal beam scanner in the quasi-simultaneous multiplane imaging system, the prism was placed before the AOD so that the incident beam at the prism remained stationary introducing the negative group delay dispersion (GDD) required to cancel the positive dispersion induced in the AOD (see Fig. 1(a)). However, to compensate for the dispersion utilising a prism, the procedures of positioning the prism can be divided into two stages. The first stage is to determine the correct incident angle of the laser at the prism to compress the distorted beam shape, while the second stage is to determine the correct separation between the prism and the AOD to minimize the broadened pulse duration.
To function in the Bragg regime as an optical scanner, the first order diffraction angle of AOD is defined as [28] 1st where θ 1st is the first order diffraction angle, λ is the laser wavelength, f is the carrier frequency of the acoustic wave and V is the velocity of the acoustic wave. From Eq. (1), we can derive the spatial dispersion constant, σ AOD to be For the AOD model chosen (DTSX-400-980, AA Optoelectronic, France) in developing the multiplane functional imaging system, the corresponding central carrier frequency, F c at the laser wavelength 900 nm is 87.5 MHz and the acoustic velocity, V is 650 ms −1 . All analyses for the spatial and temporal dispersion compensation were conducted with reference to this central frequency of the AOD and the ultrafast laser wavelength of 900 nm. Based on Eq. (2), the calculated spatial dispersion constant, σ AOD is 0.00771°/nm. By rotating the prism and thus defining the angle of incidence of the laser, the spatial dispersion induced by the AOD can be cancelled out based on the condition that [26] 0 AOD prism σ σ where σ prism is the negative spatial dispersion constant of prism. σ prism being [27] prism d dn dn d where β is the exit angle of the laser from the prism, n is the refractive index of the prism and dn dλ is the prism chromatic dispersion. The detailed derivation of d dn β can be found in Ref [27]. At 900 nm, the corresponding values of n and dn dλ for SF11 glass are 1.760 and −0.427°/nm respectively. Here, in our prism-AOD compensation analysis, we consider only the magnitude of dn dλ . At the given apex angle, α, of the prism, i.e. 60°, the progression of the spatial dispersion constant with increasing incident angle can be plotted to find the intersection point at which both the values of σ prism and σ AOD equate and thus, helping to establish the correct angle of incidence of the laser at the prism for beam shape recovery. In our instance, the optimum laser incident angle estimated is 55.6°.

prism and t negative GDD
e of the laser pr nge of the resul m and the AOD y anisotropic a rdinary axis a [29]. As a res dinary axes wa guide to determ nce, Eq. (6) pr D. In this insta n in Fig. 2 where τ out is the output pulse width after the prism-AOD, τ in is the input pulse width, GDD AOD is the positive GDD of the AOD and GDD prism-AOD is the resultant negative GDD generated by the prism-AOD pre-compensation unit with incremental L distance as expressed by Eq. (6). On the basis that the value of GDD AOD parameter was 6250 fs 2 as provided by the manufacturer and the τ in value was fixed at 131.5 fs, the final output pulse duration was calculated. In this instance, we momentarily discounted the difference in the pulse width between the initial and the optimal pre-compensation conditions as it did not contribute to the variation in the final pulse width with the increment in the prism-AOD distance. As depicted in Fig. 5(c), the change in the pulse duration with increasing prism-AOD distance as observed experimentally is in good agreement with the predicted trend, albeit there is a small offset between the trough positions at which the minimum pulse width was measured. This is because it can be difficult, in practice, to precisely measure the actual distance between the prism and the AOD.

Quasi-simultaneous multiplane microscopy construction
The quasi-simultaneous multiplane functional imaging system was built around a Sutter Moveable Objective Microscope (MOM, Sutter, USA) that offers a slimline microscope frame with accessible window to the resonant scanner, which allows easy hardware integration for additional bespoke imaging modalities (see Fig. 6). A femtosecond Ti:Sapphire laser (Mai Tai BB, Spectra-Physics, USA) tuned to 900 nm was used as the twophoton excitation source. The components that made up the add-on multiplane functional imaging modality primarily consisted of the DTSX-400-980 AOD for fast inertia-free optical switching, the SF11 equilateral prism for pre-compensation of AOD material dispersion and the C330TMD-B aspheric lenses for high NA remote focusing. The normal of the prism was fixed at ~56° with respect to the incident excitation laser at which angle the focused beam spot was detected to be the smallest using the CMOS camera. The prism was placed ~25 cm prior to the AOD at which distance the resultant pulse width after propagating through the AOD was measured to be the shortest using a collinear autocorrelator. The remote focusing system comprised two face-to-face C330TMD-B aspheric lenses with the first lens, AL1 mounted on a 3-axis fine translation stage (MBT616D/M, Thorlabs, USA) while the second lens, AL2 was fixed in position. The acoustic frequency of the AOD was programmed to switch between 87.5 ± 4 MHz, i.e. 83.5 MHz and 91.5 MHz respectively, to provide two distinct optical paths: (1) one bypassed the remote focusing system leading to the nominal focus; (2) the other encompassed the refocusing system leading to the axial focal displacement. Both beam paths were then recombined with a polarising beamsplitter. The AOD access time in the microsecond range permitted near simultaneous imaging of two focal planes at different depths in vivo. A cascade of 4f telescopic imaging systems were constructed utilising pairs of achromatic doublets so as to reimage the pupil plane of the aspheric lens onto the objective lens. Given that in vivo imaging generally suffers some degree of specimen motion, especially in the axial direction, it is desirable to have an extension of the depth of focus so that the neurons of interest stay in the image, even in the presence of specimen movements. For this reason, the beam was expanded to partially fill the back aperture of the objective lens to about 50% of the aperture diameter. This created an extended axial focus with an approximate length of 12 µm. The emitted fluorescence was captured by the full NA of the objective lens, thus maintaining the detection efficiency. This configuration pre-emptively makes the multiplane functional imaging more robust to the specimen motion, maintaining the focus on the active neurons during imaging over a period of time and th brain.

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Remote
Because, in multiplane im separated by m range of ~40 relative 2P ex fluorescent b embedded in through the tr efficiency is collected over (n = 10 samp intensity at th  We observed no marked differences in the lateral resolution -the value remained largely around ~1.6 µm across various scan depths. Compared to the theoretical estimation of ~1.1 µm for the half-filled objective lens, the lateral resolution determined empirically appears to be lower. From Fig. 7(a), it can be seen that the axial size of the PSF is minimum, i.e. ~13.7 µm, at the zero refocusing and starts to broaden as the displacement of the focal spot from the nominal focal plane increases. The initial axial resolution measured at the zero refocusing is slightly lower than the predicted with the value of ~12.5 µm. These experimental observations can be attributed to the incomplete cancellation of the higher order phase terms at the objective pupil plane by the less perfect reimaging condition between the high NA aspheric singlet lens and the water dipping compound objective lens, added to the possible presence of the residual spatial dispersion from the AOD. Therefore, the wavefront distortion, predominantly the longitudinal spherical aberration, further manifested itself as the spread of the axial intensity distribution of the PSF, when the distance between the aspheric lenses in the remote focusing system is either increased or decreased to shift the focal spot away from the nominal plane. Apart from that, the scattering effect in the 3D bead sample can also lead to the elongation of the axial PSF especially when the excitation beam is refocused deeper into the sample and thus, contributing to the loss of symmetry in the excitation efficacy over the refocusing depth as illustrated in Fig. 7(b). As we intended to create images with an extended depth of focus, these extra PSF broadening effects were not considered to be detrimental to the imaging task.

In vivo quasi-simultaneous multiplane calcium imaging of mouse somatosensory cortex
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Funding
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