1. Introduction

Optical imaging is an essential tool in biology because of its ability to spatially resolve sub-cellular details with high molecular contrast. With the advent of commercial solutions for laser scanned confocal and multiphoton microscopy, high-resolution optical imaging has evolved from a specialized technique for optical scientists to a tool commonly used by biologists for everyday experiments[1]. This widespread acceptance combined with advances in chemistry and genetics has generated great interest in the development of new contrast agents[2] and new methods for imaging in general[3]. There is now a growing set of contrast agents that spans a wide collection of targets, from proteins to cell populations[4]. For instance, the use of antibody-targeted exogenous fluorescent agents or chimeric fluorescent proteins[2] in transgenic animals enable to follow very specific populations of cells and proteins in their native environment[5]. However, two aspects may lead to deleterious artifacts. First, the use of exogenous labels or of chimeric proteins can ultimately affect the function of the tagged proteins themselves. Moreover, one can not exclude that the over-expression of chimeric proteins to obtain sufficient fluorescent signals may have adverse effects on the cellular physiology. These techniques have nevertheless become very powerful and are unavoidable tools for understanding cell signaling pathways, cellular physiology and physiophatology[6]. However, some structures can be difficult to label. For instance, cell membranes can be impermeable to dyes and can make dye penetration difficult. For these reasons, endogenous contrasts have also been investigated as a mean to overcome some of the limitations of exogenous labelling. Several such contrast methods are already used for biological applications: fluorescence of endogenous molecules[7], second-harmonic generation (SHG) of noncentrosymmetric structures[8], and spontaneous Raman scattering from endogenous vibrations[9]. In the last decade, coherent anti-Stokes Raman scattering (CARS) microscopy has gained significant attention in biological imaging because of its biochemical specificity and its higher sensitivity at high molecular concentration compared to spontaneous Raman microscopy[10, 11]. By combining two laser beams of different optical frequencies, it becomes possible to resonantly drive the vibration of a molecule to produce an anti-Stokes photon that carries the chemically-specific information. This signal can be orders of magnitude larger than that obtained with spontaneous Raman microscopy, at high molecular concentration, and can be almost comparable to fluorescence. This sensitivity makes it possible to combine this technique with video-rate microscopy and benefit from a high-frame rate for live animal imaging for example[12]. The application of CARS microscopy to lipid imaging has provided a very successful technique to image lipid-rich structures such as sebaceous glands[12], adipocytes[12] and myelin sheaths[13, 14] without the use of any exogenous labels. However, the nonlinear enhancement arising from CARS microscopy comes at the cost of complexity: two lasers are needed, the nonlinear interaction with the molecules depends on the polarization of the incident beams and the generated signal is quadratic with the molecular concentration[10]. This is particularly limiting for quantitative imaging since the structure orientation with respect to the lasers polarization affects the signal strength[14] which in turn affects the morphometric parameters that can be extracted with image analysis. In the case of myelin imaging, this means the amount of signal depends on the membranes orientation since the long lipid chains are always aligned perpendicular to the latter[15].

In this paper, we will demonstrate quantitative morphometry of myelin in rat white matter spinal cord tissue with a robust optical technique that alleviates the polarization dependence of the CARS signal intensity. Our procedure uses a combination of circularly polarized laser beams to produce CARS images with minimal polarization dependence. This method avoids the acquisition of multiple images with post-processing for recovering a polarization-independent myelin signal. Moreover, it allows the correlation of the pixel value with the square of the density of myelin and makes images suitable for morphometric interpretation using standard semi-automatic computer-assisted data analysis tools. This technical approach based on the endogenous signal of myelin promises to be optimal for real-time in vivo structural imaging of healthy or pathological tissue.

2. Materials and methods

2.1. Laser light source for CARS imaging

The laser system (Fig. 1(a)) consists of an Optical Parametric Oscillator (OPO) (Levante Emerald, APE-Berlin) pumped by a frequency-doubled Nd:Vanadate mode-locked laser (High-Q Laser, Austria). The pump laser generates a 7 ps, 80 MHz pulse train of 532 nm and 1064 nm laser light. The OPO utilizes a temperature-tuned LBO nonlinear crystal for parametric oscillation and is pumped with 5.5 W of 532 nm laser light. In order to probe the CH₂ symmetric stretch vibrations of lipids (2845 cm^-1), we use the signal from the OPO (tuned to 816.8 nm) as the CARS Pump beam with a fraction of the 1064 nm laser as the Stokes beam. To control the states of polarization (SOP) of the excitation beams at the sample, a device for compensating ellipticity introduced by dichroics is required for both laser beams (Fig. 1(a)). The SOP of both laser beams is controlled using a combination of a half-wave plate (Tower Optical Corporation, AO15Z 1/2 817 and AO15Z 1/2 1064) and a quarter-wave plate (Tower Optical Corporation, AO15Z 1/4 817 and AO15Z 1/4 1064) (see section 3.2). The beam sizes are individually adjusted using a telescope so that they overfill the objective back aperture. The Pump beam (OPO, 816.8 nm) and the Stokes beam (1064 nm) are then overlapped in space using a dichroic long-pass filter (Semrock, LP02-1064RU-25) and in time using a delay line before they are sent collinearly to the laser scanning microscope. In order to avoid photodamage of the spinal cord tissue, the average power of the Pump and Stokes beam at the sample is limited to 40 mW and 25 mW, respectively.

 

Fig. 1. (a) Laser system for CARS imaging. HWP_p: half-wave plate at the Pump wavelength, HWP_s: half-wave plate at the Stokes wavelength, QWP_p: quarter-wave plate at the Pump wavelength, QWPs: quarter-wave plate at the Stokes wavelength, T_p: telescope for the Pump beam, T_s: telescope for the Stokes beam, DL: delay line, DF₁: recombining dichroic filter, DF₂: detection dichroic filter, MO: microscope objective, SPF: short-pass filter, BPF: band-pass filter, L: lens and PMT: photomultiplier tube. (b) Cross section view of a myelin sheath (only one wrapping is shown). E_p: Pump electric field amplitude, E_s: Stokes electric field amplitude and θ is the angle between the laboratory x-axis and the direction of the linear polarization of the excitation beams. (c) Diagram of transverse and longitudinal imaging planes. (d) Evolution of the state of polarization of the excitation beams (either pump or Stokes) at the various positions labeled in (a). Dotted lines are the fast and slow axes of the HWP and QWP respectively. DF combines the effects of both dichroic filters DF₁ and DF₂.

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2.2. Epi-detection scheme

The CARS images are acquired using a modified commercial beam-scanning microscope (Olympus, IX71/FV300) with a long working distance 60X (NA 0.9) water immersed objective (LUMPlanFI/IR, Olympus). The backscattered anti-Stokes signal (662.8 nm) is collected in the epi-direction[12]. It is separated from the Pump and Stokes beams by a dichroic long-pass filter (Semrock, FF735-Di01-25x36) and spectrally filtered of unwanted residual light using a combination of two laser block filters (Semrock, FF01-750/SP-25) and a band-pass filter (Semrock, FF01-655/40-25). A red-sensitive photomultiplier tube (Hamamatsu, R3896) is used as a non-descanned epi-detector (Fig. 1(a)) in the external detector position, 12 cm apart from objective.

2.3. Preparation of fixed spinal cord tissue and slices

All experimental procedures have been performed in accordance with guidelines from the Canadian Council on Animal Care. Male Sprague Dawley rats of 280–350 g body weight (Charles River Laboratories, Wilmington, MA) were killed by intracardiac perfusion with 4% paraformaldehyde (PFA, Fischer Scientific, Pittsburgh) in 0.1 M phosphate buffer (PB), pH 7.4, under deep anesthesia. The spinal cord was extruded, and post-fixed overnight in 4% PFA. The lumbar enlargement was isolated, rinsed several times with 0.1 M PB. 1 mm thick transversal slices were made with a vibratome (Leica, VT 1000).

2.4. Preparation of live spinal cord tissue and slices

In cases where live tissues were required, animals were deeply anesthetized by 4% isoflurane and immediately decapitated. The spinal cord was rapidly removed by hydraulic extrusion and immersed in a cold oxygenated (95% O₂, 5% CO₂) artificial cerebrospinal fluid (ACSF) solution containing the following (in mM): 126 NaCl, 2.5 KCl, 2 MgCl-, 2 CaCl₂, 1.25 NaHPO₄, 26 NaHCO₃, and 10 glucose. The lumbar spinal enlargement was isolated, and maintained in continuously oxygenated ACSF solution for at least 20 min prior to CARS imaging experiment.

When spinal cord slices were required for the imaging experiment, rats were briefly perfused transcardially before decapitation, with a ice-cold oxygenated ACSF containing (in mM): 252 sucrose, 2.5 KCl, 6 MgCl^-, 1.5 CaCl₂, 1.25 NaHPO₄, 26 NaHCO₃, 10 glucose, and 5 kynurenate. 1 mm thick slices were cut from the isolated lumbar spinal enlargement in the transversal plane using a vibratome, and were allowed to recover for 15–30 min in an immersion chamber. Slices were then transferred to an oxygenated ACSF solution described above. After 1 h of recovery, individual slices were transferred to a IX71 compatible recording chamber (RC-26G, Harvard Apparatus) and continuously superfused (1–2 ml/min) with this oxygenated ACSF.

2.5. Semi-automatic computer-assisted morphometric analysis of myelinated axons

In-house software, implemented in MATLAB, has been developed for computing morphometric parameters. The state-of-the-art method for computing morphometric information from myelinated axons, developed for histology on ultra-thin slices of fixed tissue, consists in thresh-olding an image and seek for boundaries using a recognition algorithm[16]. The boundaries are identified using a sliding threshold set by the user manually. Those boundaries are then used to make various measurements such as the fiber and axon area, the fiber and axon diameter, the g-ratio (ratio of the axon diameter to the fiber diameter), the myelin thickness and the myelin area are computed[17, 18].

3. Physical description

3.1. Theoretical analysis of CARS signal generation in myelin

Myelin, the electrically-insulating sheaths surrounding the axons in the peripheral nervous system and mainly in the white matter of the central nervous system, is a wrapping of phospholipid bilayers essentially composed of about 75% lipids and 25% proteins. In a rat, each bilayer has a typical thickness of approximately 10 nm. A standard sheath is constituted of approximately 80 wrappings of individual bilayer providing a total thickness of myelin of around 1 µm[19]. Lipids are essentially made of long chains (z-axis) of CH2 that are perpendicular to the membrane (x-axis). All phospholipids are angularly distributed about the carbon chains (z-axis) without any preferential direction[20]. This means that in the CH2 plane (x-y plane) all the molecules are uniformly oriented, granting the myelin sheaths a macroscopic rotation symmetry axis (z-axis) that is perpendicular to the myelin membrane (Fig. 1(b)), only the first wrapping is shown). Each microscopic molecule of CH₂ forms an orthorhombic unit cell, which has an mm ₂ point group symmetry characterized by a two-fold rotation axis plus two mirror planes that contain the axis of rotation. The macroscopic third-order susceptibility associated with this symmetry has 21 independent nonzero elements; 3 elements with indices all equal (χ 3 _xxxx, χ ³ _yyyy, χ ³ _zzzz) and 18 coefficients with indices equal in pairs[21]. Since the CARS process is far from an absorptive electronic resonance, further simplification is possible by applying explicitly Kleinman’s symmetry arguments[22] and using the contracted notation for third-order nonlinear effects[23], leading to macroscopic third-order susceptibility with only 4 independent nonzero elements: c₁₁, c₃₃, c₁₆ and c₁₈, respectively corresponding to indices xxxx, zzzz, xxzz and xxyy. There are two planes possible for imaging as shown on Fig. 1(c): transverse (used with sliced tissue) and longitudinal (used for whole spinal cord). Assuming that the propagation axis is perpendicular to the transverse plane of the myelin sheath cylindrical geometry (Fig. 1(b)) and that both lasers pulses are linearly polarized in that plane, the CARS signal intensity can be calculated. The excitation polarization dependence of the CARS signal intensity of myelin is:

where E_p and E_s represent the Pump and Stokes electric field amplitudes respectively and θ is the angle between the laboratory x-axis and the direction of the linear polarization of the excitation beams. Eq. (1) clearly shows that the CARS signal intensity possesses an angular modulation generating excitation polarization dependence. Since the direction of the linear polarization of the excitation beams is fixed, variations in the signal intensity occur when the orientation of the lipid membranes varies. In particular, excitation polarization dependence appears while imaging myelin cross sections or tortuous longitudinal myelin sheaths.

A similar mathematical development can be performed assuming that both lasers are circularly polarized in the transverse plane. In this case, the CARS signal intensity can be expressed as:

It is clear from Eq. (2) that the angular modulation of CARS signal intensity has been removed. Because of the point group symmetry (mm2) of the myelin sheaths and the direction of propagation, no additional terms are probed with circular polarizations. This method yields CARS images intrinsically free of excitation polarization dependence since a circular polarization is an average projection on every tensor elements and the tensor elements do not vary in intensity throughout the image (only their orientations change). Note that the polarization of the emitted light does not affect the detected intensity since no element in the detection path is polarization sensitive (detectors or dichroic). With the procedure explained below, images of myelin cross sections can be made more uniform such that they can be used for quantitative analysis. For images in the longitudinal plane (Fig. 1(c)), the polarization dependence cannot vanish completely with circular polarization because the orientation of the lipid chains changes with imaging depth which alters the combination of accessible tensor elements. Nevertheless, the use of circular polarization in this case also reduces the polarization dependence to allow a more accurate quantitative analysis.

3.2. Polarization ellipticity compensation

Precise control over the polarization of the excitation beams at the sample is challenging due to the presence of dichroic filters downstream from those adjustments. The differences in amplitude of reflection and transmission coefficients between the s and p polarization axis (|R_s|≠|R_p| and |T_s|≠|T_p|) of the filters as well as the introduction of a phase shift (δ) between these two polarization components can alter the SOP, introducing ellipticity to the excitation beams. The usual solution, proposed by Chu et al.[24], uses linear polarization and is not feasible in vivo since it requires rotating the samples. The need for specimen rotation has been removed in a recently proposed solution generating linear polarizations with high-extinction ratio[25], for SHG microscopy in rat tail tendon fibrils.

Using a similar approach, it is possible to show mathematically that polarization ellipticity compensation, for the generation of circular polarizations, is also feasible (illustrated in Fig. 1(d)). Using the same notation as in the previous study[25], a circular polarization at the sample is achieved when:

where δ represents the phase shift for light polarized along the p-polarized with respect to light polarized along s-polarized axis, β is the angle of the quarter-wave plate’s slow axis relative to the s-polarized axis, ϕ(ϕ=α-β) is the angle between the excitation polarization after the half-wave plate and the slow axis of the quarter-wave plate and α is the angle between the excitation polarization after the half-wave plate and the s-polarized axis. The circularity of the CARS Pump and Stokes beams, at the sample, has been verified before every imaging session with a rotating polarizer (Thorlabs, LPVIS100). Both SOP were circular within a deviation of less than ±5 % (power ratio of the semi-minor to the semi-major axis of the polarization ellipse).

3.3. Other approaches to minimize the excitation polarization dependence of the CARS signal

Very recently, a solution has been proposed by Fu et al.[26], to cancel the excitation polarization dependence of the CARS signal in myelin. This approach involves the offline mathematical recombination of two images acquired with orthogonal linear polarizations. However, the description of sections 3.1 and 4.1 shows that three tensor elements (c₁₁, c₁₆ and c₃₃) contribute to the CARS signal generation, which implies that the solution proposed by Fu et al.[26] is an approximation since it only considers one term of the full tensor expression (c₁₁). A better but tedious method using linearly polarized excitation beams consists in rotating the polarization in the x-z plane by small increments while recording an image for each value of θ. Thereafter a pixel-by-pixel maximum intensity projection is performed (offline) to get the signal coming from the angle at which the lasers polarization and the membranes are collinear. This approach effectively cancels the excitation polarization dependence of the CARS signal, but it is not suitable for in vivo applications because it requires taking many images at the same location with different linear polarizations. On the other hand, our approach based on circularly polarized laser beams produces CARS images with minimal polarization dependence without any post-processing. Alternatively, it could be possible to rapidly modulate the linear polarization angle of the excitation beams and use phase-locked detection to measure the maximum signal together with its associated phase shift. This would provide quantity and orientation of the lipid chains in a single measurement, in a way similar to what was reported in SHG microscopy for collagen fibers[27]. However, this is technically very challenging for a dual beam system such as a CARS microscope and was not implemented since the lipid chain orientation is not needed for morphometry.

4. Results

4.1. Quantification of the excitation polarization dependence of myelin CARS signal

Figure 2(a) and Fig. 2(b) show transverse sections of myelinated axons from the white matter of fixed spinal cord tissue recorded with linearly and circularly polarized laser beams. The angle between the macroscopic x-axis of the myelin sheaths and the direction of the linear polarizations of the beams varies around the axons, inducing a systematic excitation polarization dependence of the CARS signal (see inset of Fig. 2(a)). On the other hand, the use of circular polarizations for excitation removes most polarization dependence (see inset of Fig. 2(b)), since it probes all available tensor elements and essentially averages out the polarization dependence. In images of parallel-running axons from the white matter of live spinal cord tissue (Fig. 2(c)), the polarization dependence of the CARS signal is much less important but still present. The large scale alignment of the fibers gives an approximately constant value of θ in Eq. (1) and automatically minimizes polarization effects. However, regions where fibers are not exactly parallel to each other show this polarization dependence (see the encircled zones on Fig. 2(c) and Fig. 2(d)). This is particularly important when studying pathological cases such as multiple sclerosis and nerve injuries[13] where large scale alignment of the myelin sheaths is not expected to be preserved.

The excitation polarization dependence of the myelin CARS signal intensity can be quantified with high-resolution images of a single cross section of myelin from the white matter of live spinal cord tissue acquired with the excitation beams linearly polarized along two orthogonal axes (Fig. 3(a) and 3(b)). Regions around the axon where the CARS signal is larger correspond to recorded pixels where the polarization of both beams is parallel to the myelin membrane. A plot of line profiles centered on the axon and taken at 1° increments shows absolute maxima occurring at 180° apart, when the excitation beams are linearly polarized perpendicular to the long and oriented molecular chains of CH₂. Conversely, non-zero minima are seen when the excitation beams are linearly polarized perpendicular to the myelin membrane. This observation is consistent with the work of Potma et al.[15] on single lipid bilayer, but differs from the model proposed by Fu et al.[26] which predicts a vanishing CARS signal for myelin membrane oriented perpendicularly to the polarization of the excitation beams.

 

Fig. 2. Example of the excitation polarization dependence of the CARS signal of myelin. (a) and (b) Myelin images from transverse sections of fixed spinal cord, acquired with the excitation beams linearly polarized and circularly polarized respectively. (c) and (d) Myelin images from longitudinal sections of live spinal cord tissue at the equatorial plane, acquired with the excitation beams linearly polarized and circularly polarized respectively.

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On the other hand, when using circularly polarized laser beams, the intensity of all pixels is not modulated by any excitation polarization effects (Fig. 4(a) and Fig. 4(c)), as would be expected from Eq. (2). The plot of line profiles for live and fixed myelin sheaths recorded with circularly polarized excitation beams is shown on Fig. 4(b) and Fig. 4(d) respectively. Those images are free from excitation polarization dependance and the pixel values are directly proportional to the square of the density of myelin within the focal point and therefore more suitable for morphometric data analysis.

4.2. Morphometric information of myelinated axons using circularly polarized laser beams

In the literature, it is common to assess the structural characteristics of myelinated axons with four plots of parameters measured on transversal cuts of spinal cord tissue[16, 17, 18] (described in section 2.5). First, the caliber histogram (Fig. 5(b)) provides accurate information on the size distribution of axons. Second, the scatter plot of the g-ratio as a function of the axon diameter (Fig. 5(c)) is of paramount importance since it reflects either the type of nerves studied or the presence of a pathological state[17]. For example, the presence of thinly myelinated axons (high g-ratio) is common to many pathological states and regenerating fibers. Linear regression on the scatter plot of the axon diameter versus the fiber diameter (Fig. 5(d)) permits computation of the g-ratio. Finally, the scatter plot of the myelin area as a function of the fiber diameter (Fig. 5(e)) is also of prime significance in the examination of remyelinating axons[28].

Although transverse cuts of spinal cord provide a large number of axons with which to perform morphometric analysis with good statistics, it is often preferable to obtain morphometric data from live uncut tissue to avoid preparation and cutting artifacts. This can be performed on intact (contact-free) spinal cord with the acquisition of a z-stack followed by three-dimensional reconstruction, thanks to the optical sectioning provided by CARS imaging. Figure 5 shows such a reconstruction from 29 images (240 µm×240 µm, total depth=14 µm) of live spinal segment acquired with the excitation beams circularly polarized. From this three-dimensional reconstruction, 39 orthogonal views perpendicular to the parallel-running axons (5 µm apart) have been generated with the freely accessible Volume Viewer plugin. A typical example is shown on Fig. 5(a) and a short animation displaying the full set is available as supplemental multimedia content (Multimedia 1). From these orthogonal views, 180 morphometric measurements (on 20 different parallel-running axons) have been performed in order to characterize the axons from a specific region of the spinal cord in its native state. Figure 5(b)–(e) summarizes our results using the collection of graphics described earlier. First, from the histogram of caliber classes for the 180 morphometric measurements (Fig. 5(b)), it is found that all axon diameters range between 3.5 µm and 9.5 µm with a mean axon diameter of 6.78±1.19 µm. Then, the scatter diagram of the g-ratio versus the axon caliber (Fig. 5(c)) reveals variations in g-ratios between 0.5 and 0.65 and a minor trend to increase with the axon caliber. The third plot (Fig. 5(d)) allows the direct computation of the mean g-ratio which was found to be 0.57±0.04 (R=0.90). Finally, Fig. 5(e) relates the myelin area to the fiber diameter and shows that the probed nerve population is in a non-pathological state since no splitting or y-shaped distribution is observed[28].

 

Fig. 3. Quantification of the excitation polarization dependence of the CARS signal of a single cross section of myelinated axon from live spinal cord tissue. The images (a) and (b) have been acquired with the excitation beams linearly polarized along two perpendicular directions. (c) The expression for the theoretical excitation polarization dependence of the CARS signal intensity has been superimposed (black continuous line) to the experimentally measured polarization dependence (red dots).

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Fig. 4. A single cross section of myelin from a transverse slice of live (a) and fixed (c) spinal cord tissue are shown. (b) and (d) Illustrate the angular distribution of the normalized CARS signal for the myelin cross section shown in (a) and (c) respectively.

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5. Discussion

5.1. Validation of the theoretical model of the excitation polarization dependence

The experimentally measured linear polarization dependence was fitted with the three non-vanishing elements of the macroscopic third-order susceptibility of Eq. (1) as free parameters. As can be seen from Fig. 3(c), the theoretical model follows accurately the experimentally measured polarization dependence, yielding non-zero values for the three elements (c₁₁=1.00, c₁₆=0.19 and c₃₃=0.48) that contribute to the CARS signal generation in myelin. This confirms that none of these coefficients can be excluded while seeking a method that removes the excitation polarization dependence of the CARS signal.

5.2. Chemical specificity of the CARS signal

It is well known that some fixation procedures can induce autofluorescence. For example, we observed that tissues fixed with glutaraldehyde strongly autofluoresce and mask the resonant CARS signal significantly. For this reason, a paraformaldehyde based fixation protocol was used. The autofluorescence induced by this protocol was experimentally quantified. It represents less than 5 % of the total observed signal. Special attention has been paid to ensure that the CARS signal is resonant by detuning the Pump beam by 10 nm. The nonresonant contribution of the CARS signal is very weak, measured to less than 3% of the resonant signal. When testing the theoretical model of polarization dependence on fixed tissue, the fitted values for the three elements of the macroscopic third-order susceptibility were slightly different: c₁₁=0.99, c₁₆=0.27 and c₃₃=0.57. This may be due to the autofluorescence contribution or because of membrane disruption (partial breaking of the membrane symmetry) caused by the fixation process, but it has not been investigated further.

 

Fig. 5. This set of curves displays structural informations from live spinal cord tissue with circularly polarized laser beams. (a) Typical contact-free CARS optical slice. (Media 1)(b) Histogram of caliber classes reveals that the mean axon diameter is 6.78±1.19 µm. (c) Scatter diagram of the g-ratio versus the axon caliber. The g-ratios varie between 0.5 and 0.65. (d) Plot of the axon diameter versus the fiber diameter. A linear regression reveals a mean g-ratio of 0.57±0.04. (e) Scatter diagram of myelin area to the fiber diameter. This single population curve shows that the probed nerve is in a non-pathological state.

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5.3. Use of circular polarization and its impact on CARS signal generation

The use of circularly polarized excitation beams alleviates the excitation polarization dependence on either live or fixed tissues. However, because the CARS signal scales as I ² _p I_s, special care must be exercised when circularizing the excitation beams. As shown on Fig. 4(b) and Fig. 4(d), small systematic variations remain which may be due to small deviations (less than ~5%) from perfectly circularly polarized laser beams at the sample. This has been confirmed by verifying the circularity of the CARS Pump and Stokes beams at the sample which was then compared to the normalized CARS intensity. In addition, the generated CARS signal using circularly polarized excitation beams is ~3.25 times smaller than the maximum intensity generated with linearly polarized beams (θ=0° in Eq. (1)) and ~1.33 times larger than the minimum intensity generated with linearly polarized beams (θ=90° in Eq. (1)). The images can be properly used for morphometric analysis as this modulation is minimal and their contrast is sufficient.

5.4. Native state morphometry

Myelin sheath cross sections and longitudinal myelin profiles common to many diseases can be analyzed when the image intensity is adequately representing the amount of myelin, such as what is provided with circularly polarized light. For example, on Fig. 3(a) where linear polarization is used, analysis would erroneously suggest that the myelin membrane is thinner on the left and right sides than on top and bottom sides. The inaccuracy of the g-ratio measurement would seriously limit its physiological relevance as a key parameter in the assessment of the myelin health. On the other hand, CARS images recorded with circularly polarized laser beams can be readily analyzed using boundary recognition algorithms and morphometric information can be accurately calculated (Fig. 5). The measured range between 0.5 and 0.65 can be compared with the work of Hildebrand et al.[19], where they reported g-ratios for fixed spinal cord tissue ranging between 0.65 and 0.82. However, morphometric information extracted from fixed tissue is almost certainly altered by the preparation itself (fixation and cutting artifacts). In an effort to estimate these changes, they hypothesize that the g-ratio for live spinal cord tissue should vary between 0.55 and 0.72, which is considered optimal for the conduction velocity of impulses in myelinated fibers[29]. The data on intact spinal cord tissue with our method supports this hypothesis, as shown on Fig. 5(c).

5.5. Other considerations for the circular polarization method

The generation of CARS optical histologic slices (contact-free) from three-dimensional reconstructions enables the examination of tissue in its native state. However, when performing reconstructions with z-stack in the longitudinal plane, a residual CARS signal modulation remains around the axons, even when illuminating with circularly polarized light. This problem is unavoidable (unlike the case of transversal cuts of spinal cord tissue) since the orientation of the lipid chains relative to the polarization of the excitation beams changes continuously with the position of the imaging plane. At the surface of the axon’s cylindrical geometry, since all phospholipids are distributed perpendicular to the membrane without any preferential angle, images are free of polarization dependence whether excitation beams are circularly or linearly polarized[20]. At the equatorial plane, the situation is identical to transverse plane: the use of circular polarization cancels the polarization dependence and linearly polarized laser beams show the same excitation polarization dependence as in Eq. (1). However, different subsets of tensor elements are probed in these two cases (since the tensor element related to the y-axis, c18, is probed), and the overall average magnitude obtained with circularly polarized laser beams is different at each plane. Hence, when images are taken between the surface of the axons and their equatorial plane, the orientation of the lipid chains changes and the optical beams probe different elements of the macroscopic third-order susceptibility associated with the long carbon chains. The configuration with circularly polarized light decreases the modulation by up to 2.66 times compared to linear polarization. The small residual modulation present when imaging longitudinal section of axons does not prevent the accurate measurement of the axon’s morphometric characteristics on native state tissues. In summary, the use of circularly polarized excitation beams is always desirable since it removes the polarization dependence wherever the geometry allows it, and minimizes it in other cases. Finally, the CARS signal is also influenced by the diminishing laser power due to propagation losses into the tissue as the depth increases. Although this effect is not related to the polarization of the incoming beams, the scattering due to white matter is the limiting factor determining imaging depth.

5.6. Outlook

Typically, assessment of myelin health using morphometric parameters is obtained from histopathology on ultra-thin slices of fixed tissues with brightfield imaging or electron microscopy[19]. Performing longitudinal studies to follow the progression of a disease with this method is tedious at best due to the complexity of sample preparation and processing combined with the poor tissue sampling. Methods for the exogenous labelling of myelin in vivo have been developed[30] but it is well known that the use of dyes could perturb the biological system under investigation and dye penetration into the myelin is an issue. In this respect, label-free imaging techniques have many major advantages over other imaging modalities. CARS microscopy is particularly interesting for the study of demyelinating diseases such as multiple sclerosis, an autoimmune disease where the immune system attacks the central nervous system, leading to the destruction of the electrically-insulating myelin sheaths surrounding the axons. The exact details leading to the disease are still an active area of research and many animal models are used to study its progression. CARS microscopy provides the required framework that will open the way to large scale longitudinal studies and ultimately to a better understanding of the disease.

6. Conclusion

In conclusion, a robust optical technique that alleviates the excitation polarization dependence of the CARS signal intensity has been successfully implemented in our laboratory and extensively tested on fixed and live rat spinal cord tissue. With this strategy, the CARS intensity within the focal volume is more homogenous throughout images, leading to more accurate measurements of the morphometric characteristics of the myelin under investigation. This has been used on live spinal cord tissue to compute morphometric analysis of healthy myelinated axons in their native state. Our approach provides quantifiable endogenous signal which can be used to assess myelin health using standard morphometric techniques and has the potential to become a powerful tool in the quest to understand demyelinating diseases.