Light-sheet microscopy in thick media using scanned Bessel beams and two-photon fluorescence excitation

Light-sheet microscopy in thick media using scanned Bessel beams and two-photon

Light-sheet microscopy in thick media using scanned Bessel beams and two-photon fluorescence excitation 1

. Introduction
The generation of high-quality three-dimensional images in large scattering media such as tissue, embryos, plants, or cell clusters in biology is a tricky task. Limited penetration and scattering of illumination light inside the specimen degrade the image quality. Moreover, unnecessary photo-bleaching of fluorophores that are not in the image plane degrade the usability of microscopes. In this context, light-sheet based microscopy [1] offers the decisive advantage that only those parts of the object are illuminated that are in the plane of focus of an objective lens (OL). Sample illumination by a thin sheet of light reduces fluorophore bleaching significantly relative to conventional epi-fluorescence microscopy or point-scanning confocal microscopy. Recently it has been shown that an alternative form of light-sheets can be generated by using laterally scanned Bessel beams [2][3][4][5], which revealed an increased penetration depth of illumination light in thick media of up to 50% [2,3]. However the advantage of beam self-reconstruction in scattering media is at the cost of a decreased image contrast: the Bessel beam's ring system, which contains the photons necessary for beam-healing, excites fluorescence above and below the plane of focus. Exploiting the propagation stability of Bessel beams allowed to increase image contrast very efficiently. The confocal-line detection principle, where out-of-focus fluorescence excited by the ring system is largely blocked [6] also rejects scattered light. Therefore, this principle is also useful in combination with Gaussian beam illumination [7,8].
However, an alternative approach would be desirable, where a thin light-sheet does not generate any out-of-focus fluorescence. Two-photon excitation (TPE) of the fluorophores is such a method that avoids the contrast degrading effect of the ring system. In TPE, two near-infrared (NIR) photons must hit the same fluorophore at the same time to excite it [9]. The resulting quadratic dependence of the fluorophore emission F(r) on the illumination intensity h ill (r) is expected to suppress the fluorescence in the ring system efficiently. In addition, the nearly doubled wavelength of the NIR excitation light should reduce scattering and increase the penetration depth similarly to point scanning TPE fluorescence microscopy [10][11][12]. The favorable combination of light-sheet microscopy and TPE has been employed by other groups using static light-sheets [13], scanned Gaussian beams [14] and Bessel beams [4,5]. Moreover, TPE by Bessel beams in point-scanning systems were used, but only to increase the depth of focus of the system [15,16]. The results presented here are the first investigation of TPE by Bessel beams in thick and strongly scattering media using a light-sheet microscope. This combination is especially interesting since on the one hand the light-sheet microscope is an ideal tool to study the propagation of beams in scattering media because the propagation of illumination light within the detection focal plane can be observed from the side. On the other hand, only at depths of several hundred microns inside scattering media the following three advantages can take effect efficiently: the reduced photo-bleaching enabled by light-sheet microscopy, weaker scattering artifacts due to the self-reconstruction capability of the Bessel beams and increased contrast due to the TPE principle.
We demonstrate the performance of this approach in tumor cell clusters. The motivation for observing this form of cancerous tissue in a light-sheet microscope is the following: The discovery of new anticancer drugs requires High Throughput Screening (HTS) approaches. These are usually based on animal models, which generally well recapitulate the main features of human tumors. 2D-cell based in-vitro models have been extensively used in preclinical drug screening despite their poor predictive capability for in-vivo efficacy. 3D-tissue culture models, on the other side, are undisputedly better candidates to reconcile scientific, medical and ethical requirements. Multicellular Tumor Spheroids (MCTS), which were shown to be superior in-vitro tumor models as compared to 2D cell monolayers, have not yet received widespread application in cancer biology. Beside the technical difficulty of massively producing size-controlled spheroids, another limitation for their more extensive use originates from the difficulty to image thick and highly scattering samples with reduced photo-toxicity over several days. To decipher the molecular and cellular mechanisms of (in-vitro) tumor progression, imaging techniques are required that allow investigating not only the rim of peripheral cells, but also the core of the spheroid, to fully observe the spatial and temporal organization of the whole tumor mimics.
In this paper we describe briefly the technical setup of a microscope able to fully image tumor multicellular spheroids. We explain and illustrate all necessary principles and give a detailed mathematical description of the simulated and measured results or phenomena. We compare the non-diffraction capability of single (1p) and two (2p) -photon fluorescence excitation Bessel beams in homogeneous media as well as their self-reconstruction properties in scattering media. We analyze contrast and resolution for both beam types. In the last section of this paper, we demonstrate the strong benefits of 2p-Bessel beams both in widefield and confocal-line detection mode -for light-sheet microscopy in 250µm large biological tumor cell clusters.

Experimental setup
In order to be able to compare the performance of various beams for linear and non-linear fluorescence excitation in a light-sheet microscope we expanded our existing setup (which is described in detail in [3]) by a Ti-Sapphire-Laser (Chameleon, Coherent). This laser emits short pulses with a duration of 140fs with a repetition rate of 80MHz with high power (P avg > 1W) over a wide range in the near-infrared spectral range (720nm to 920nm). The setup for TPE fluorescence is sketched in Fig. 1. A switchable mirror allows quick alteration between illumination by the visible lasers and the NIR laser. All optical elements (mirror, lenses) are suitable for the usage in the NIR range and for the high peak intensities generated by the pulsed laser. Even though the achromatic doublets (Qioptiq) are optimized for the visible spectral range, neither reflections due to the imperfect anti-reflection coating nor aberrations to the illumination beams were observed. A broadband LCOS-based spatial light modulator (SLM) was chosen (Pluto NIR II, Holoeye) which is optimized for a wide spectral range (400-1100nm) and thereby enabled us to compare phase shaped beams in the visible and NIR range. For all measurements, a 40x/0.8 lens (W Achroplan, Zeiss) was used.

Light-sheets by scanned illumination beams and resulting fluorescence
In the following, we investigate both theoretically and experimentally the fluorescence excitation of differently labeled objects. The fluorophore distribution c F (r) at position r inside the illuminated part of the object can be either constant, c F (r) = c 0 , as in the case of a homogeneous fluorescein solution. Alternatively, c F (r) can vary abruptly as in the case of fluorescent spheres in a non-fluorescent medium or non-fluorescent spheres embedded in a fluorescent gel. And third, c F (r) can vary relatively smoothly as in the case of stained dense cell clusters. The resulting fluorescence intensity distribution F(r) is modulated by c F (r), by the excitation cross section σ 1p for linear and σ 2p for two photon excitation, as well as by the excitation intensity h ill (r). We find both for the linear and for the non-linear fluorescence: Since two photons have two arrive independently of each other during the life-time of the fluorophore's virtual excitation state, the photons' probabilities to hit the fluorophore's cross  F(x, y) for different types of illumination beams with the same depth of field along the illumination z-axis. A Gaussian beam for one-photon (1st column) and two-photon excitation (2nd column) and a Bessel beam for one-photon (3rd column) and two-photon excitation (4th column). a) Single beam fluorescence intensity F(x, y, 0) and the corresponding line scans F(0, y, 0) on the right. b) Light sheet fluorescence produced by a lateral scan F(x, y, 0) dx of the three beams in x-direction and line profiles F(0, y, 0) dx| x=0 through the light-sheets. c) Multiplications of the light-sheets with the detection point-spread function h det (x, z).
section must be multiplied with each other. This results in the quadratic dependence of the illumination intensity, h ill,2 (r) 2 , as described in Eq. (2). For the typical case of pulsed illumination light, a more precise description of the temporally averaged fluorescence would be F 1p (r) = c F (r) · σ 2p · G · h ill,2 (r) 2 , where G is a correction factor [9]. However, keeping this in mind and disregarding dispersive effects, we hold on to the expression of Eq. (2).
In many cases, the resulting fluorescence F(r) in a homogeneously stained sample illustrates well the excitation intensity h ill (r), if the detection PSF is small enough. Figure 2 displays simulation results of linear and nonlinear fluorescence excitation by Gaussian beams and Bessel beams at λ 1 and λ 2 , respectively. The depth of field of the fluorescence excitation ∆z = 100µm is equal for all beams. As described in the Appendix, due to the different wavelengths used, the illumination beams, h ill,1 (r), and h ill,2 (r), have to be designed differently to match their depth-of-field. The cross sections, F(x, y, z = 0) and the intensity line scans F(0, y, 0) reveal the relatively large widths of the Gaussian beam (green line), the narrow main lobe of the Bessel beam with distinct side lobes from the ring system (blue line) and the narrow profile of the two photon (2p) Bessel beam (red line), where the rings are strongly suppressed.
By continuously displacing the illumination beam h ill (r) by b x in lateral x-direction the re-sulting 1p-and 2p-fluorescence distributions are These dependencies are displayed in Fig. 2(b) for the four types of beams and a homogeneous fluorophore concentration c F (r) = c 0 . The profiles F scan (0, y, 0) through the light-sheet in the right part of Fig. 2(b) reveal the increased width of the light-sheet relative to the width of a single beam for the 1p-Bessel beam. This effect is hardly visible for the 2p-Bessel light-sheet.
In the last step of the image generation process, fluorescence is detected by the detection objective (DO) with NA det and point-spread function h det and imaged onto the camera. Mathematically, the 3D image p(b y , r) for a light-sheet shifted vertically by b y is obtained by where * denotes the convolution, which corresponds to a low-pass filtering of the fluorophore distribution F(b y , r) especially along the detection y-axis. The images read The image of a point-like fluorophore, c F (r) = c 0 δ (r) illuminated by a light-sheet at position b y = 0 is shown in Fig. 2(c) and demonstrates the suppression of out-of-focus fluorescence for the 2p-Bessel beam, but not for the 1p-Bessel beam.
The numerical results are confirmed experimentally by the 2D-images of single beams , focused at NA ill ≈ 0.3, that excite fluorescence in a homogeneous fluorescein solution. As demonstrated by the experimental data shown in Fig. 3, single-photon fluorescence excitation generates strong fluorescence in the Bessel beam's ring system shown in Fig. 3(a), which is still well visible due to the narrow h det (r) at a Numerical Aperture NA det = 0.8 of the detection lens. In the two-photon case, fluorescence from the ring system is strongly suppressed as can be seen in Fig. 3(b), which is also shown by the lateral profiles through the beam images shown in Fig.  3(c).

Light scattering during propagation through inhomogeneous media
In most applications of light-sheet microscopy the refractive index variations inside the object are not index-matched (cleared). Illumination and detection light are scattered at each refractive index change, which leads to a new propagation direction of each scattered photon. Only a small fraction of the photons remain unscattered, so-called ballistic photons, while the other photons are scattered very many times such that these photons become diffusive. The corresponding electromagnetic field of the illumination beam is split into an incident and a scattered electric field, E i (r) and E s (r), such that the fluorescence intensity F 1p (r) ∝ h ill,1 (r) can be expressed as: Corresponding to Eq. (1), these equations show that the illumination intensity h ill (r) can be split into two terms: h i (r) and h s (r) both illuminate the object [17]. Thereby two images are generated by convolution of the object c F (r) with the detection PSF: The second image is called the ghost image and needs to be minimized by clever illumination or detection techniques. In the two-photon case the sum of the ideal and the scattered illumination beams can be expressed as The first term in Eq. (9) corresponds to Eq. (2), whereas the second term represents unwanted two-photon fluorescence excitation in the object. In the two-photon case the ghost image can be expressed mathematically as Theoretically, p ghost approaches a minimum when the illumination beam intensity becomes minimal or when the following two terms approach each other h 2 s,2 (r) → 2 · h i,2 (r) · h s,2 (r). In the linear case, the Bessel beams ring system illuminates many spheres outside the Bessel beams main lobe. For TPE, fluorescence excitation by the ring system and by scattered light is suppressed so that mainly spheres along a thin line corresponding to the Bessel beams main lobe are visible.
The fluorophore distributions described by Eq. (7) and Eq. (9) were measured by using a cluster of fluorescent 0.75µm polystyrene spheres embedded in a slightly fluorescent gel as shown in Fig. 4. Whereas in the single-photon case the Bessel beam excites a lot of unwanted fluorescence, i.e. fluorescence outside the main lobe of the Bessel beam, this unwanted fluorescence is hardly visible in the two-photon case.

Artifacts in non-linear light-sheet microscopy
A quadratic fluorescence dependence on the excitation intensity has two effects. On the one hand it suppresses the unwanted fluorescence in a controlled manner, for example from the Bessel beam ring system. On the other hand, it might increase image artifacts such as the frequently occurring stripes resulting from the interference of scattered and unscattered light. To investigate the strength of the two effects, we used the beam propagation method (BPM) [18,19] to simulate the propagation of various illumination beams through a cluster of non-fluorescent glass spheres with a diameter d = 2µm that are embedded in a fluorescing environment. From the expressions in Eq. (7) and Eq. (9) describing the fluorescence distribution for linear and non-linear excitation, respectively, we derived the ghost image in Eqs. (8) and (10). The results for horizontal and vertical cross-sections, p(x, y 0 , z) and p(x 0 , y, z), through the 3D image stacks are displayed in Fig. 5(a)-(d). By simulating the ideal image, shown in Fig.  5(e) that results from illumination by a homogenous, non-scattered light-sheet with a thickness of only 0.2µm, we can easily generate the unwanted ghost image by subtraction of the real image (compare Eq. (8)). The lateral standard deviations of the ideal and the ghost image as a function of the propagation distance z are shown in Fig. 5(f) and (g), respectively (see also [2]). From these values we can estimate the image quality by calculation of the parameter Q art , which we define as follows: A good light-sheet generates high contrast in the ideal image (ŝ ideal is large) and a low contrast in the ghost image (ŝ ghost is small). By inspecting Fig. 5, one can recognize two things: illumination in the case of the 2p-Bessel beam results in the highest value Q art = 0.66 and secondly, most sphere images, especially those indicated by white arrows (i and ii), are reproduced at best by the 2p-Bessel beam image. LUT of the images is auto-scaled so that they express the relation between the amplitude of the artifacts and the images of the spheres. Note that no information on the absolute image contrast can be drawn from these images. f, g) the lateral standard-deviation of the ideal and the ghost image for all four imaging modes, according to Eq. (14) derived in [2]. Q art gives the ratio of the total lateral standard-deviations of the ideal and the ghost images according to Eq. (14).

Resolution and contrast in a scattering sample
To assess resolution and image contrast inside of a scattering medium we image a volume containing fluorescing polystyrene spheres (diameter 0.75µm). The spheres were embedded in nonfluorescent gel and imaged for linear and nonlinear fluorescence excitation by Bessel beams at NA ill ≈ 0.3. An image projection ∑ y p(x, z) along the detection y-axis is shown in Figs. 6(a,d) together with a projection ∑ x p(y, z) along the beam-scanning x-axis in Figs. 6(b,e). It can be clearly seen that sectioning and axial resolution is greatly enhanced over a distance of more than 300µm by nonlinear fluorescence excitation over linear excitation by a Bessel beam. The images of the spheres are significantly smaller along the detection axis without any remarkable degradation along the propagation direction (Figs 6(b,e)). The two image magnifications shown in Figs 6c, f reveal the shape and the extent of the sphere images, which come close to the expected shapes of the detection point-spread-function h det (r). This confirms that beam selfreconstruction works well in large scattering media both for single-photon and two-photon excitation.
The signal-to-background ratio p S /p BG (z) as well as the axial resolution dy 1/e (z) are analyzed in more detail using profiles through images of ≈ 1200 spheres. We fitted a Gaussian function to each profile p(y) extracted at the (x, z)-position of a sphere as in [6]. Figure  7(a) shows that the signal-to-background ratio p S /p BG (z) is significantly higher than in the case of two-photon excitation revealing only a small drop-off for high propagation distances z > 250µm. By analyzing the axial 1/e-widths of the bead images, dy 1/e , we find an average width of dy 1/e ≈ 2µm for the single photon illumination, whereas for TPE the average widths dy 1/e ≈ 1µm are by a factor of two smaller. Note that over a propagation distance of more than 300µm hardly any drop-off in resolution is visible.

Light-sheet imaging of tumor multicellular spheroids using two-photon fluorescence excitation
The so far discussed image quality parameters such as resolution, contrast, scattering artifacts, or light-sheet penetration depth have been investigated theoretically or by computer simulations and have been confirmed by experiments using bead clusters. However, although their ideal images remain unknown, high-quality imaging of large, scattering biological specimen is the primary goal in fluorescence microscopy. Clusters of cancerous cells (so-called tumor multicellular spheroids) represent an optimal biological test object because of their compact, spherical shapes and sizes of some 100 microns in diameter. The average scattering coefficient of the spheroids is such that reasonable imaging from only one direction is possible, but on the other hand beam spreading is well visible and the self-reconstruction capability of Bessel beams are of great advantage. A deeper understanding of the mechanisms of spheroid growth will require investigating the main cellular components, such as actin filaments, that contribute to cell shape and motility. Here, we used tumor multicellular actin-labeled spheroids stained with Alexa-488 coupled to Phalloidin. We cultivated wild-type mouse colon carcinoma CT26 cells (American Tissue Culture Collection, ATCC CRL-2638). The spheroids were prepared by encapsulating and growing cells in spherical nutrient-permeable hydrogel shells up to a spheroid size of about 250µm in diameter. The cell-containing capsules were formed by a home-made co-extrusion device. The hydrogel is made of sodium alginate (FMC, Protanal LF200S) which is a biocompatible polysaccharide. Spheroids were then embedded in agarose gel cylinders and then illuminated with two different scanning Bessel beams at wavelengths of λ 1p = 488nm and λ 2p = 920nm. Figure 8 shows images p(x, y 0 , z) of the same layer of a tumor multicellular spheroid illuminated with three different illumination beams. The images were acquired in a plane s y = 120µm inside the spheroid as indicated by the inset of Fig. 8(a). Illumination with Bessel beams provides more signal in the back part of the spheroids. This finding is confirmed quantitatively by the integrated image intensity line scans p(z) = ∑ i p(x i , y 0 , z)dx shown in Fig. 8(d). The penetration depths of the Bessel beams of d Bessel,1p ≈ 338µm and d Bessel,2p ≈ 562µm (exponential fits p ∝ exp{−z/d} in Fig. 8(d)) are enhanced by a factor of 2.2 and 3.7 relative to the penetration depth d Gauss,1p ≈ 152µm of the Gaussian beam. The increase in penetration depth for Bessel beams by a factor of 1.7 is close to the theoretical prediction for predominantly Mie-Scattering samples made in the previous section (Eq. (12)).

Increased image contrast by confocal line detection
In addition, the contrast is best for the two-photon Bessel beam, i.e. the details provided by single cells in the back part of the spheroid, are best visible with two-photon excitation. A more detailed contrast analysis is possible by investigating the ratio of high-frequency and low-frequency image information. Corresponding to the method of Truong [14], the images p(x, z) are Fourier transformed top(k x , k z ) = FT [p(x, z)] and separated into images with high spatial frequencies (HSF, where k r = k 2 x + k 2 y ≥ k F ) and low spatial frequencies (LSF, where k r = k 2 x + k 2 y ≤ k F ) defined by the corner frequency k F = 1/2µm. The ratio of the average The corresponding two-photon fluorescence excitation profile is F 2p (z) = c F · σ 2p · h ill,2 (z) 2 = c F · σ 2p · I 2 0,2 · sinc(2π · z/∆z 2p ) 4 .
For the approximation the expansion for small values of ε can be used, since ε < 1 by definition. From eqns (18) and (19) above and taking into account that different wavelengths are used to excite the same dye by linear and two-photon processes, the ratio of the depth of field for linear and nonlinear fluorescence excitation is ∆z 1p /∆z 2p = 1.39 · λ 2 /λ 1 . To obtain 1p-and 2pfluorescence excitation profiles F(z) with equal depth of field the NA and/or the ring parameter ε can be adapted. An equal depth of field ∆z 1p = ∆z 2p requires adaptation of the ring thickness parameter according to The latter approximation is valid for a constant numerical aperture NA 1 = NA 2 and when λ 2 = 2λ 1 .