Impact of wavefront distortion and scattering on 2-photon microscopy in mammalian brain tissue

Abstract

Two-photon (2P) microscopy is widely used in neuroscience, but the optical properties of brain tissue are poorly understood. We have investigated the effect of brain tissue on the 2P point spread function (PSF₂p) by imaging fluorescent beads through living cortical slices. By combining this with measurements of the mean free path of the excitation light, adaptive optics and vector-based modeling that includes phase modulation and scattering, we show that tissue-induced wavefront distortions are the main determinant of enlargement and distortion of the PSF₂p at intermediate imaging depths. Furthermore, they generate surrounding lobes that contain more than half of the 2P excitation. These effects reduce the resolution of fine structures and contrast and they, together with scattering, limit 2P excitation. Our results disentangle the contributions of scattering and wavefront distortion in shaping the cortical PSF₂p, thereby providing a basis for improved 2P microscopy.

Fig. 1

Comparing the effects of static, statistically homogeneous scattering and wavefront distortion on excitation photons in 2P microscopy. Brain tissue is made of particles of a wide range of size and refractive index. Particles that are smaller than the wavelength of light create a statistically homogeneous effect. This decreases the power of ballistic photons while leaving the wavefront undistorted. Particles whose size is larger than the wavelength of light induce wavefront distortion.

Fig. 2

Two-photon point spread function (PSF_2P) characteristics in the cortex. (a) (Top left panel) experimental setup consisting of water immersion objective and beads used to measure the optical system PSF_2P. Single images of beads acquired using the optical system in the focal plane (x-y) (Bottom left) and in a plane comprising the optical axis (z) (Bottom right). y axis indicated by a dashed line in the bottom left panel. Excitation wavelength (λ) = 725 nm. (b) (Top left panel) Experimental setup used to measure the PSF_2P in acute slices of cortex. (Bottom left panel) 3D sketch of the cortex showing in blue a tangential slice in cortical layer II / III. (Top middle and right panels) x-y and y-z images of beads acquired by focusing through tangential slices at a depth of 150 μm. y axis indicated by a dashed line in the top middle panel. Same look up table as (a). (c) Gaussian fits of average PSF_2P. (Top panel) x-y plane (Bottom panel) z axis. Error bars show the standard deviation.

Fig. 3

Excitation mean free path in the cortex. (a) Maximum intensity projection along the z axis of a z-stack in layer II / III showing Alexa 488 filled pyramidal cell with dendrites spanning 200 μm in x-y and 84 μm in z. The scattering length or mean free path of excitation light (L_se) was estimated from the fluorescence of the dendrites at different depths. (b) Relationship between the fluorescence (F) divided by the square of the laser Power (P) and normalized by its value at the cortical slice surface (β) versus depth. L_se was calculated from an exponential fit (line) at a wavelength of 725 nm. (c) Dependence of L_se on wavelength (n = 4 −8 cells). Error bars give the standard error of the mean (sem), which is smaller than the symbols for λ ≤ 850 nm.

Fig. 4

Effect of scattering on the PSF_2P. (a) Conventions used when modeling the PSF_2P. Ballistic photons form a cone that can be decomposed into beamlets of coordinates (r = sinθ / sinθ_ΝΑ, ω). (b) Comparison of the x_e and y_e profiles of the measured cortical PSF_2P with the theoretical, microscope and modeled PSF_2P that accounts for the effect of L_se in the focal plane (Top panel) and along the optical axis (Bottom panel).

Fig. 5

Conventional implementation of deformable membrane mirror (DMM). (a) Schematic diagram of conventional DMM implementation. (b) PSF_2P of the microscope including the DMM in control conditions in the focal plane (Top) and in a plane comprising the optical axis (Bottom) indicated by the dashed line on the top panel.

Fig. 6

Fluorescence and SNR enhancement of the PSF_2P in the cortex with a DMM. (a) (Top left panel) Experimental setup used to measure the PSF_2P in acute slices of cortex. (Bottom panel) 3D sketch of the cortex showing in blue a thalamocortical brain slice. (b) Single images of a bead acquired using the DMM in control conditions (CC) in the focal plane (top panel) and in a plane comprising the optical axis (z) (bottom panel, y axis indicated by dashed line in top panel) at a depth of 150 μm. (c) As for B but for the optimized mirror shape in the cortex (OMSc). Same laser power as (b). (d) Intensity projection (sum) of the z-stack of images of the bead shows that, in this example where there was no visible surrounding lobes, DMM optimization resulted in a decrease of the volume of the main lobe of the PSF_2P and decrease in the background.

Fig. 7

Spatial dependence of wavefront correction for the conventional DMM configuration. (a) Experimental protocol: an optimization was performed at the center of the field of view (1), at a particular cortical location. The cortical location was moved across the field of view at distances of 50 μm (position 2) or 100 μm (position 3) away from the optical axis and the fluorescence and SNR obtained using the optimized mirror shape (OMSc) and in control conditions (CC) were measured. The change in fluorescence (b) and SNR (c) across the field of view using the OMSc performed at position 1. There was no significant change in these parameters with distance to the optical axis (p > 0.08, paired t-test). Grey symbols: individual experiments, colored symbols: mean, black bars: sem.

Fig. 8

Spatial dependence of wavefront distortions in the cortex. (a) (Left) A group of beads imaged through a 150 μm thalamocortical slice for the DMM set to control conditions (CC). The DMM shape was optimized on the central bead giving the optimized mirror shape in the cortex (OMSc). (Right) Using OMSc improved bead definition and fluorescence intensity in the lower half of the image but not in the upper half of the image, illustrating that wavefront distortions vary across a cortical slice. (b) Protocol used to examine the variability of wavefront distortions in the cortex: a first cortical column (C1) was positioned at the center of the field of view (indicated by the square box) and a first DMM shape optimization was performed there, giving OMSc (1). Then a neighboring cortical column (C2) was positioned at the center of the field of view, a second DMM shape optimization was performed, giving OMSc (2). Last a bead at the center of C2 was imaged using OMSc (1), OMSc (2) and CC. (c) Bead fluorescence using OMSc (1) was significantly smaller than using OMSc (2) (*) (p < 0.011, n = 8, paired t-test). Grey symbols: individual experiments, colored symbols: mean. The sem is smaller than the colored symbols.

Fig. 9

Compensating for optical aberrations with light-efficient DMM implementation. (a) Light efficient configuration with the DMM implemented at 45°. (b) PSF_2P of the microscope with the light-efficient DMM in control conditions in the focal plane (Left) and in a plane comprising the optical axis (Right). Y axis indicated by the dashed line on the top panel. (c) Single images of a bead under a cortical slice at a depth of 150 μm acquired using the DMM in control conditions (CC) in the focal plane. (d) As for (c) but for the optimized mirror shape in the cortex (OMSc). Same laser power as (c). (e) Z stacks of images of the previous bead were acquired and normalised to the maximal fluorescence for the DMM in CC. Focal plane (top panel) and plane comprising the optical axis (z) (bottom panel). Arrow indicates a surrounding lobe that disappeared after the DMM optimization. x axis indicated by dashed line in top panel. (f) Same as (e) but using the OMSc. (g) Maximum intensity projection (MIP) of data from (e). (h) MIP of data from (f).

Fig. 10

Spatial dependence of wavefront correction for the light efficient DMM configuration. (a) Experimental protocol: an optimization was performed at the center of the field of view (position 1), at a particular cortical location. The cortical location was moved across the field of view at distances of 50 μm (position 2) or 100 μm (position 3) away from the optical axis, and the fluorescence and SNR obtained using the optimized mirror shape (OMSc) and in control conditions (CC) were measured. (b - c) The change in fluorescence (b) and SNR (c) across the field of view using the OMS performed at position 1. There was no significant change in these parameters with distance to the optical axis (p > 0.17, paired t-test). Grey symbols: individual experiments, colored symbols: mean, black bars: sem.

Fig. 11

Optimization of the DMM shape on a cellular element. (a) Fine dendrite imaged with DMM in control conditions (CC). (b) Fluorescence change during the DMM shape optimization on a dendrite (arrow in panel A). (c) Same cellular element imaged using the optimized mirror shape (OMSc) and the same laser power as in CC.

Fig. 12

Contributions of wavefront distortion and scattering to the cortical PSF_2P and their effects on 2P microscopy. (a) Image of modeled microscope PSF_2P assuming NA 0.7 in x-y plane (top) and y-z plane (bottom panel), y axis indicated by dashed line in top panel. (b) Example of a modeled PSF_2P taking into account the optical aberrations corrected using the DMM in the cortex assuming NA 0.7. 2P excitation was normalized by its maximal value in (a) and (b). (c) Quantification of the average 2P excitation (integral of the distribution of the squared intensity of excitation light in the PSF_2P) in the central 3D Gaussian lobe and in the surrounding lobes, for the modeled ideal PSF_2P, the measured microscope PSF_2P, the modeled PSF_2P including measured cortical distortions and the experimentally measured cortical PSF_2P, all at NA = 0.7. (*) p < 0.003, t-test, (**) p < 0.001, t-test. (d) Modeling the effects of wavefront distortions and scattering on fluorescence. (Top panel) The predicted fluorescence emitted by homogeneously labeled spherical objects using an ideal microscope, in the presence of scattering (L_se = 77 μm) and in the presence of optical aberrations, plotted versus the size of the object. Furthermore, to determine effects of the surrounding lobes, the fluorescence emitted by the main Gaussian core of the PSF_2P was calculated in the presence of optical aberrations (dotted red line). (Bottom panel) Plots from top panel were normalized to the maximum value.