Quantitative myelin imaging with coherent anti-Stokes Raman scattering microscopy: alleviating the excitation polarization dependence with circularly polarized laser beams.

Abstract

The use of coherent anti-Stokes Raman scattering microscopy tuned to the lipid vibration for quantitative myelin imaging suffers from the excitation polarization dependence of this third-order nonlinear optical effect. The contrast obtained depends on the orientation of the myelin membrane, which in turn affects the morphometric parameters that can be extracted with image analysis. We show how circularly polarized laser beams can be used to avoid this complication, leading to images free of excitation polarization dependence. The technique promises to be optimal for in vivo imaging and the resulting images can be used for coherent anti-Stokes Raman scattering optical histology on native state tissue.

Full text

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Quantitative myelin imaging with
coherent anti-Stokes Raman scattering
microscopy: alleviating the excitation
polarization dependence with circularly
polarized laser beams
E. B´ elanger1,2, S. B´ egin1,2, S. Laffray1, Y. De Koninck1,2, R. Vall´ ee1,2
and D. Cˆ ot´ e1,2,∗
1Centre de Recherche Universit´ e Laval Robert-Giffard (CRULRG), Universit´ e Laval,
Qu´ ebec, QC, G1J 2G3, Canada
2Centre d’Optique, Photonique et Laser (COPL), Universit´ e Laval,
Qu´ ebec, QC, G1V 0A6, Canada
∗daniel.cote@crulrg.ulaval.ca
Abstract:
tuned to the lipid vibration for quantitative myelin imaging suffers from
the excitation polarization dependence of this third-order nonlinear optical
effect. The contrast obtained depends on the orientation of the myelin
membrane, which in turn affects the morphometric parameters that can
be extracted with image analysis. We show how circularly polarized laser
beams can be used to avoid this complication, leading to images free of
excitation polarization dependence. The technique promises to be optimal
for in vivo imaging and the resulting images can be used for coherent
anti-Stokes Raman scattering optical histology on native state tissue.
The use of coherent anti-Stokes Raman scattering microscopy
© 2009 Optical Society of America
OCIS codes: (170.3880) Medical and biological imaging; (300.6230) Spectroscopy, co-
herent anti-Stokes Raman scattering; (180.4315) Nonlinear microscopy; (180.6900) Three-
dimensional microscopy
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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
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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 trans-
genic 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 ex-
ogenous labels or of chimeric proteins can ultimately affect the function of the tagged pro-
teins 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 under-
standing 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 endoge-
nous 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 biologi-
cal 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 informa-
tion. 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] with-
out 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 sig-
nal 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
beamstoproduceCARSimageswithminimalpolarizationdependence. Thismethodavoidsthe
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.
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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 Emer-
ald, 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
1064 nm 816.8 nm
HWPP
QWPP
HWPS
QWPS
DF1
TS
DL
Scanning microscope
TP
SPF
DF2
BPF
L
Cross section of
spinal cord tissue
MO
PMT
(a)
(b)
Axon
(no myelin)
Myelin
(phospholipid bilayer)
z-axisEp,Es
θ
x-axis
(c)
ABC
α/2
α
β
φ
ˆ p
α
ββ
A HWPB QWP
CDFMO
ˆ s
(d)
Fig. 1. (a) Laser system for CARS imaging. HWPp: half-wave plate at the Pump wave-
length, HWPs: half-wave plate at the Stokes wavelength, QWPp: quarter-wave plate at the
Pump wavelength, QWPs: quarter-wave plate at the Stokes wavelength, Tp: telescope for
the Pump beam, Ts: 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). Ep: Pump electric field amplitude, Es:
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 DF1and DF2.
laser light. The OPO utilizes a temperature-tuned LBO nonlinear crystal for parametric oscil-
lation and is pumped with 5.5 W of 532 nm laser light. In order to probe the CH2symmetric
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
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the states of polarization (SOP) of the excitation beams at the sample, a device for compen-
sating 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, AO15Z1/2817 and AO15Z1/21064) and a quarter-wave plate (Tower Optical
Corporation, AO15Z1/4817 and AO15Z1/41064) (see section 3.2). The beam sizes are indi-
vidually 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.
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 (Sem-
rock, 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) solu-
tion 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 per-
fused 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
transversalplaneusingavibratome,andwereallowedtorecoverfor15–30mininanimmersion
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.
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2.5. Semi-automatic computer-assisted morphometric analysis of myelinated axons
In-house software, implemented in MATLAB, has been developed for computing morphome-
tric 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 sys-
tem and mainly in the white matter of the central nervous system, is a wrapping of phospho-
lipid 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 approx-
imately 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 CH2that 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 CH2plane (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
wrappingisshown).Each microscopicmoleculeofCH2formsanorthorhombic unitcell,which
has an mm2 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
(χ3
is far from an absorptive electronic resonance, further simplification is possible by applying ex-
plicitly 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, c16and 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 propaga-
tion 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 in-
tensity can be calculated. The excitation polarization dependence of the CARS signal intensity
of myelin is:
?
xxxx, χ3
yyyy, χ3
zzzz) and 18 coefficients with indices equal in pairs[21]. Since the CARS process
Ilinear
ωas(θ)
∝
E4
cos2θ?3c16+cos2θ[c11−3c16]?2?
pE2
s
sin2θ?c33+cos2θ[3c16−c33]?2+
,
(1)
where Epand Esrepresent 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 po-
larization 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 ap-
pears while imaging myelin cross sections or tortuous longitudinal myelin sheaths.
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A similar mathematical development can be performed assuming that both lasers are circu-
larly polarized in the transverse plane. In this case, the CARS signal intensity can be expressed
as:
Icircular
ωas
s
∝1
8E4
pE2
??c11+3c16
?2+?c33−3c16
?2?
.
(2)
It is clear from Eq. (2) that the angular modulation of CARS signal intensity has been re-
moved. 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 polariza-
tion 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
(|Rs| ?= |Rp| and |Ts| ?= |Tp|) 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 elliptic-
ity 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:
tan(2φ) =sin(2β)
tan(δ),
(3)
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 rela-
tive 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 polariza-
tion dependence of the CARS signal in myelin. This approach involves the offline mathematical
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recombination of two images acquired with orthogonal linear polarizations. However, the de-
scription of sections 3.1 and 4.1 shows that three tensor elements (c11, c16and 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 polar-
ized 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 mat-
ter 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 po-
larizations 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 circu-
lar 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 de-
pendence. 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 quanti-
fiedwithhigh-resolutionimagesofasinglecrosssectionofmyelinfromthewhitematteroflive
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 observa-
tion 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.
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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.
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] (de-
scribed 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 stud-
ied 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 re-
gression 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 per-
form morphometric analysis with good statistics, it is often preferable to obtain morphometric
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(c)
a)
(a)
b) (b)
0 50100150
Angle [°]
200 250 300350
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Normalized CARS intensity
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).
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 measure-
ments (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) summa-
rizes 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].
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(b)
(c) Fixed(d)
(a) Live
050100 150
Angle [°]
200 250300350
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Normalized CARS intensity
050100150
Angle [°]
200250300350
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Normalized CARS intensity
Fig. 4.A singlecrosssectionof myelinfroma transverseslice oflive(a) andfixed (c)spinal
cordtissueareshown.(b)and(d)IllustratetheangulardistributionofthenormalizedCARS
signal for the myelin cross section shown in (a) and (c) respectively.
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 con-
firms 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 repre-
sents 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 contribu-
tion 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
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(d)
Axon diameter, circular [um]
(c)
(e)
(b)
1 um
345678910
0
5
10
15
20
25
30
35
Axon diameter, circular [um]
Absolute frequency
345678910
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Axon diameter, circular [um]
g−ratio
68
Fiber diameter, circular [um]
10121416 18
3
4
5
6
7
8
9
10
68 10 1214 16
20
40
60
80
100
120
140
160
Fiber diameter, circular [um]
Myelin area [um2]
(a)
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.
process, but it has not been investigated further.
5.3.Use of circular polarization and its impact on CARS signal generation
The use of circularly polarized excitation beams alleviates the excitation polarization depen-
dence on either live or fixed tissues. However, because the CARS signal scales as I2
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 us-
ing 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.
pIs, special
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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
whatisprovidedwithcircularlypolarizedlight.Forexample,onFig.3(a)wherelinearpolariza-
tion 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 rang-
ing 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 re-
constructions 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 re-
mains 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
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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 com-
bined withthe poor tissuesampling. Methods forthe exogenous labelling ofmyelin invivo 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 mi-
croscopy 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.
Theexact detailsleading tothediseasearestillanactive areaofresearchand many animalmod-
els 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 exten-
sively 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.
Acknowledgments
We want to thank H. Dufour for his technical assistance on custom image analysis software
and electronics and M. Lessard-Viger for his help with figures. This work was supported by
the National Science and Engineering Research Council of Canada (NSERC-CHRP), Canadian
Foundation for Innovation (CFI), Canadian Institutes of Health Research (CIHR-CHRP), Cana-
dian Institute for Photonics Innovation (CIPI). D. Cˆ ot´ e is the holder of a Canadian Reasearch
Chair in Biophotonics. E. B´ elanger is a recipient of a NSERC Ph.D. scholarship. S. B´ egin is
the holder of a FQRNT Ph.D. scholarship.
(C) 2009 OSA 12 October 2009 / Vol. 17, No. 21 / OPTICS EXPRESS 18432
#113834 - $15.00 USDReceived 8 Jul 2009; revised 1 Sep 2009; accepted 12 Sep 2009; published 28 Sep 2009