Mimicking Multimodal Contrast with Vertex Component Analysis of

Mimicking Multimodal Contrast with Vertex Component Analysis of Hyperspectral
CARS Images
Joel T. Tabarangao and Aaron D. Slepkov
Department of Physics and Astronomy, Trent University
Peterborough, Ontario, Canada
[email protected]
[email protected]
In this work, we show the applicability of vertex component analysis (VCA) of hyperspectral CARS
images in generating a similar contrast profile to that obtained in “multimodal imaging” that uses
signals from three separate nonlinear optical techniques. Using an atherosclerotic rabbit aorta test
image, we show that the VCA algorithm provides pseudocolor contrast that is comparable to
multimodal imaging, thus suggesting that under certain conditions much of the information gleaned
from a multimodal nonlinear optical approach can be sufficiently extracted from the CARS
hyperspectral stack itself. This is useful for unsupervised contrast generation on hyperspectral
CARS implementations such as multiplex CARS that may not have multimodal capabilities. The
utility of VCA as a quantitative analysis tool in CARS is also addressed.
1. Introduction
The importance of nonlinear optical microscopy techniques based on vibrational resonances has
rapidly grown over the past decade. At the forefront of these set of imaging tools is Coherent AntiStokes Raman Scattering (CARS) Microscopy [1-4]. As depicted schematically in Figure 1, CARS is a
four-wave mixing process involving the interaction of pump ( ), Stokes ( ), and probe ( )
photons to yield a higher energy anti-Stokes photon ( ), the production of which is stimulated in
a sample when the difference of the pump and Stokes angular frequencies matches a vibrational
resonance ( = − ). Thus, CARS is a label-free imaging technique with broad chemical
specificity. The stimulated nature of this nonlinear optical process means that in a wide range of
conditions CARS signals are orders of magnitude larger than those from traditional spontaneous
Raman scattering [5]. Therefore, a primary advantage of CARS as a microscopic technique lies in
vastly improved image acquisition times. While traditional CARS microscopy research laid the
foundation for it as a powerful contrast-based (i.e. qualitative) technique, there has been a
considerable recent thrust to develop the quantitative aspects of this and other coherent Raman
microscopy techniques [6-10].
Traditionally, CARS microscopy has been implemented using pulsed picosecond lasers which are
optimal for this technique because the picosecond pulse bandwidth closely matches the Raman
linewidths of relevant molecular resonances [11,12]. However, pulsed femtosecond laser
approaches to CARS are currently popular for various reasons including the fact that their high
peak powers enable “multimodal” operation that simultaneously integrates CARS with other
nonlinear optical imaging tools such as second harmonic generation (SHG) and two-photon
excitation fluorescence (TPEF), among others, to provide unique contrast information [13]. SHG, for
example, is sensitive to non-centrosymmetric molecular assemblies such as collagen, and TPEF can
map endogenous fluorescent molecules such as elastin. Figure 2(a) shows such a multimodal image
of an atherosclerotic rabbit aorta sample.
Another primary advantage of femtosecond-laser-based approaches to CARS lies in their inherently
broadband pulses which allow for better harnessing of the spectroscopic power of vibrational
imaging. The combination of spectroscopy and microscopy, termed “hyperspectral imaging”, can
provide spectral information at every pixel with a multitude of unique chemically-specific contrasts.
Figure 2(b) represents a single image from a hyperspectral CARS stack from a sample of
atherosclerotic rabbit aorta tissue, with two representative spectra shown for a bright and a dark
pixel. Typically, contrast is achieved either by on-peak (i.e. single frequency) imaging, such as
shown in this figure, or by comparing ratiometric differences in two or more peaks in the spectra
that are diagnostic of the molecule being probed [14,15]. There is a growing sense, however, that
single- or few-frequency analysis of hypespectral CARS images makes insufficient use of the rich
spectral information inherent to the technique. Thus, more sophisticated spectral analysis tools—
largely based on multivariate analysis (MVA) techniques—are currently gaining in prominence [1618].
Multivariate analysis is a mainstay in “chemometrics” and is increasingly being used for vibrational
imaging of biological samples [7,14,16,18]. For Raman and infrared absorption microscopy, MVA is
used primarily for qualitative chemical identification using colormaps. By contrast, CARS and other
coherent Raman microscopy techniques have faster acquisition rates that provide impetus for its
use not only for qualitative contrast but also quantitative concentration measurements that are
useful for monitoring dynamic concentration changes in biological samples[8]. Principal component
analysis (PCA) is one of the popular clustering multivariate tools used in both Raman and CARS
microscopy [16,17]. PCA clusters spectra based on their similarities by choosing basis sets that
have the most variance and which are linear combinations of the original spectral axes. PCA,
however, traditionally only provides classification based on spectral similarities but not
quantitative information.
Although the CARS signal increases with concentration, the presence of a non-resonant background
(NRB) that coherently combines with the Raman lineshape yields nonlinear concentration
dependence, and is a major obstacle for quantitative CARS analysis [12]. This may, however, be
overcome using phase-retrieval algorithms that extract (or “retrieve”) the Raman lineshape [19,20].
A recent study uses a phase-retrieval algorithm and “non-negative matrix factorization” to perform
quantitative CARS microscopy [6].
Vertex Component Analysis (VCA) is another candidate for the quantitative analysis of
hyperspectral CARS Images. VCA is a spectral unmixing MVA algorithm initially developed for
remote sensing to extracts the “purest” spectra [21]. Each pixel in the hyperspectral image is
expressed as a linear combination of the pure spectral components (known as endmembers) in an
abundance fraction matrix that may be further explored for quantitative analysis. The abundance
fraction matrix may also be used to form colormaps that aid in image visualization.
In this paper, we compare a multimodal image that makes use of single-frequency CARS, SHG and
TPEF modalities to extract contrast information from a complex biomedical tissue sample with an
image generated from the VCA of its associated CARS hyperspectral image data. We chose the VCA
algorithm (over PCA, for example) for two main reasons: First, unlike principal components which
do not necessarily represent a spectroscopically-identifiable object, but are rather chosen as the
most statistically distinct basis-sets, the VCA endmembers represent identifiable spectral
components, and are thus comparable to other vibrational spectra. Second, via the abundance
fraction matrix, it may be possible to extract spectral concentration information in VCA. Such
concentration information may be useful towards expanding the technique towards quantitative
CARS microscopy studies.
2. Materials and Methods
2.1. Atherosclerotic Rabbit Aorta Tissue Sample Preparation
We revisit an archival image data stack from a previous multimodal CARS microscopy study of
atherosclerotic rabbit aorta tissue[22]. The main purpose of the previous study was to investigate
the use of multimodal imaging (SHG, TPEF and CARS) for the label-free diagnosis of luminal
atherosclerosis. Hyperspectral CARS data on the same image also shows unique spectral
information on regions with contrasting multimodal signal. This stimulated our interest to recreate
a multimodal-like image using multivariate analysis of the hyperspectral image stack alone, and
compare that to the rich contrast information from the original multimodal image.
The tissue sample used in this work was provided by the National Research Council of Canada’s
Institute of Biodiagnostics. A detailed description of the sample preparation methodology, as well
as the analysis of multimodal images for this sample, is provided by Ko et. al. in Reference [22].
2.2. Optical Set-up for Multimodal and Hyperspectral CARS Imaging
Multimodal imaging was performed at the National Research Council of Canada’s CARSLab, using
the single femtosecond oscillator light-source microscopy set-up developed by Pegoraro et. al. [23].
A schematic representation of the experimental layout is shown in Figure 3. In short, a 60-fs
transform-limited laser beam centered at ~800 nm is split into two arms using a polarizing
beamsplitter (PBS). The first beam (path A) becomes the pump and probe beam. The second beam
(path B) generates a supercontinuum light in a photonic crystal fiber (PCF). The red-shifted part of
the supercontinuum that ranges from ~950-1150 nm is used as the Stokes beam for the CARS
process. An anti-Stokes signal is generated in the sample by collinearly overlapping pump/probe
and Stokes beams whose temporal-overlap-dependent frequency difference corresponds to a
vibrational resonance. For instance, the CH-stretching vibrational mode at ~2850cm-1 is probed by
overlapping in time the pump beam’s 800nm (12,500 cm-1) light with the ~1036nm (9,650cm-1)
part of the Stokes beam. The pump beam is also used to concurrently stimulate other imaging
modalities such as SHG and TPEF. The tightly focused beams are raster scanned on the sample
using galvo mirrors and the signals are detected using photomultiplier tubes (PMTs). The forwardpropagating CARS and SHG signals are filtered using a dichroic mirror and detected on separate
PMTs. The TPEF signal is detected in the backward (epi-) direction on a built-in PMT of the
Olympus Fluoview 300 microscope.
Spectral scanning is implemented by varying the temporal delay of the pump/probe beam such that
it overlaps with different portions of the Stokes light, represented schematically in Figure 3. The
spectral resolution (~30cm-1) is obtained by matching the chirps of the two pulses using high
dispersion SF-6 glass, in a process known as “spectral focusing”[23-25]. Image processing was done
with ImageJ [26], and multivariate analysis with Matlab.
2.3. Vertex Component Analysis of Hyperspectral CARS Image
VCA is an algorithm for hyperspectral unmixing that was developed in the field of remote sensing
[21]. It assumes that each spectrum in a hyperspectral dataset X (of size m x n) is a linear
combination of “pure” spectra called endmembers. That is,
X = AM + N
where M (size p x n) is the mixing matrix containing the spectra of the endmembers. A (size m x p)
is the abundance matrix containing the relative amounts of each endmember on each object in
matrix X, and N (size m x n) is the noise in the signals. In the case of a hyperspectral CARS stack, m is
the number of pixels (or “objects”), n is the number of data points (in frequency space) for each
spectrum and p is the number of desired unique unmixed spectra (or “endmembers”).
The hyperspectral image taken of the atherosclerotic rabbit aorta sample is a 256 x 256 pixel image
with 272 data points for each spectrum which translates to a 65,536 x 272 matrix. Each 256x256
image was collected in 0.58 s, and the 272 image hyperspectral stack acquisition thus required ~3
minutes. Thus, m is 65,536 pixels, n is 272 data points. The value for p may be chosen based on the
number of pure chemical substances (or anticipated “unique” spectra) in the sample. PCA itself can
be used to suggest an appropriate value for p based on how the data are clustered. We performed
VCA with p values of 3 and 4 based on the results of PCA. Details of this are discussed in the next
Each of the m pixel objects is a vector in n-dimensional space. Given a known value of p, the goal of
VCA is to determine the matrices M and A. VCA first extracts the p endmember spectra and stores
the associated endmember data points on matrix M. A vector u is selected such that no object is
orthogonal to it. All objects are projected unto u and the maximum of the projection is the first
endmember. The succeeding endmembers are iteratively projected to a subspace orthogonal to the
span of the endmembers already determined. This is done until the p endmembers are found. The
abundance fraction A is calculated by multiplying X by M#, the pseudoinverse of M.
Dealing with the CARS signal dependence on concentration is a critical first step in implementing
multivariate analysis algorithms as it affects the relative object distances in n-dimensional space
that may lead to their incorrect clustering and classification. In our work, we normalized each
spectrum to its peak (maximum) value. Another, typically robust, normalization procedure
common in spectroscopic analysis involves normalizing over the area, rather than simply over the
peak. Area normalization, however, does not seem to work well in CARS hyperspectral data analysis
because of the NRB-distorted lineshape of the CARS spectrum compared to a Raman spectrum [27].
All data analysis was performed using MATLAB 2013b with the Statistical Toolbox Package. The
calculated abundance fractions were used to generate a pseudocolor image using the RGB color
3. Results and Discussion
PCA is one of the more popular multivariate analysis tools and it is useful to compare its
performance with that of VCA. Furthermore, PCA can be used as an intermediate step for
determining the number of endmembers to input in the VCA algorithm. Figure 4(a) shows the
cumulative variance plot for the PCA of the hyperspectral CARS image of Figure 2(b). It shows that
two principal components are sufficient to account for approximately 90% of the variance in the
dataset. Further increases in the cumulative variance are insignificant after the second PC as shown
by the relatively flat profile of the cumulative variance plot from PC3 to PC6 on the same figure. The
number of PCs aids in determining the number of endmembers for VCA. With two PCs, the data can
be visualized in a score plot where the number of distinct clusters may suggest an appropriate
value for p. For our data set, as shown in Figure 4(b), there are no distinct clusters so instead we
arbitrarily based the color assignments on the four quadrants defined by the two PCs. The color
assignments (denoted in Figure 4(b)) are then the basis for the contrast shown in Figure 4(c). This
PCA image already appears somewhat similar to that of the multimodal image of Figure 2(a). For
example, the regions with strongest SHG contrast, likely collagen-rich, are easily identified in the
PCA image as well. However, little-to-no distinction is made in the PCA image between the lipid-rich
regions that appear red in the multimodal image and the green elastin-rich regions that yield strong
autofluorescence. The PCA image appears considerably coarser than the multimodal image. This is
largely because of the loss of concentration information in PCA.
Others have used PCA to extract representative spectra by averaging all the spectra from pixels of
the same cluster in an effort to identify compositionally-similar regions [16,18]. However, the
validity of this method is limited to tightly clustered groups with distinctly identifiable boundaries.
Because our 2-PC scatter plot, Figure 4(b), lacks any distinct clustering, PCA does not allow for the
extraction of representative spectra [27]. Because this single cluster is roughly centered at the
origin, it motivates a 4-quadrant PCA, and thus perhaps a 4-endmember VCA. Looking at the
retrieved PCA image of Figure 4(c), however, the red and black pixels are intermingled and are not
on distinct regions of the image. This further suggests that a 3-endmember VCA implementation
might be more effective in correctly identifying the unique spectra. And so, we performed both a 3and 4-endmember analysis of the sample as shown in Figure 5.
Figure 5(a) shows the retrieved VCA image for a 3-endmember implementation. It is immediately
evident upon inspection that the VCA image shows a stark similarity to the multimodal image in
Figure 2(a). The brightest red regions in the image match the strongest (blue) SHG regions in the
multimodal image, and are thus presumed to be vibrational signatures from collagen. In the VCA
image, however, these regions are slightly more extensive than the collagen imaged by SHG in the
multimodal image. This could be due to SHG’s sensitivity to the molecular orientation and
organization of collagen whereas CARS is more sensitive to molecular density. This makes VCA of
hyperspectral CARS imaging complementary to the SHG technique. Figure 5(c) shows the
corresponding endmember spectra for the VCA image automatically extracted from the CARS
hyperspectral data of the atherosclerotic aorta sample. In a multimodal CARS study of the same
sample, Ko et. al. highlighted similar spectra to that extracted by VCA [22]. However, those spectra
were extracted (somewhat by trial and error) using the multimodal image as a visual guide for
suggested differences in tissue character. Thus, the method was highly supervised and potentially
very time consuming. The unsupervised nature of the VCA spectral extraction, however, may be
used to an advantage for hyperspectral CARS implementations that do not usually have multimodal
imaging capability, such as multiplex CARS [2,4,28].
Figure 5(b) shows the retrieved VCA image for a 4-endmember implementation with the
corresponding four endmember spectra in Figure 5(d). It should be noted that the VCA algorithm
will always extract endmembers based on the input value for p. However, care must be taken in
judging the validity of the results. For instance, in our sample, the pixels corresponding to the
“black” endmember spectrum in Figure 5(d), highlighted by the white arrow, are confined in a very
small region on the sample, which suggests that it is not a useful endmember spectrum.
Furthermore, by inspection of the 3-endmember spectra, it appears that the black spectrum is
mostly a particular (but non-specific) combination of the red and green endmember spectra. Thus,
we conclude that despite the misleading detail found in the 4-endmember VCA image, the 3endmember VCA analysis is a better comparator to the multimodal image of Figure 2(a).
The calculated abundance fractions using the three endmembers in Figure 4(a) were used to
generate the pseudocolor image in Figure 4(b). The values of the calculated abundance fraction
ranging from 0.0 to 1.0 are used as the pixel values in Matlab’s RGB (red-green-blue) color scheme.
Thus, pixels with combinations of these three colors represent spectra that combine two or three of
the endmembers. Compared with PCA, which only assigns one color for each cluster, VCA assign
color combinations based on the spectra producing a pseudocolor image similar to the original
multimodal image.
The calculated abundance fraction also provides future prospects for use in quantitative analysis.
Using available phase-retrieval algorithms [19,20], the Raman lineshapes could potentially be
extracted by unmixing (in phase) the nonresonant background, and then used as input
hyperspectral data for VCA. It would also be interesting to compare quantitative analysis using VCA
with the recently developed FSC3 quantitative CARS method [6].
4. Conclusion
We succeeded in using an unsupervised VCA algorithm to generate contrast from a hyperspectral
CARS image of an archival atherosclerotic rabbit aorta tissue sample that is comparable to that
obtained from multimodal nonlinear optical microscopy. Furthermore, we discussed the potential
of the technique for quantitative chemical imaging with the use of abundance ratios. The usefulness
of VCA and other multivariate analysis techniques is particularly strong in powerful hyperspectral
CARS techniques—such as multiplex CARS—that do not traditionally allow for multimodal
nonlinear optical operation.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was financially supported by an NSERC Discovery Grant. The authors would like to thank
Albert Stolow and his group at the National Research Council (NRC) for the use of the Multimodal
CARS microscope and archival image stacks. We also thank Doug Moffatt of the NRC for his expert
Matlab and data analysis support. The atherosclerotic rabbit aorta samples were provided by Alex
Ko and Michael Sowa from the NRC-Institute of Biodiagnostics. The VCA program was modified
from the freely-available code supplied by J. Nascimento and J. Dias.
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Figure 1. Energy level diagram of the CARS process. ωpu, ωs, ωpr, ωas, ωR are the pump, Stokes, probe,
anti-Stokes, and Raman vibrational mode frequencies, respectively
Figure 2. (a) Multimodal image of an atherosclerotic rabbit aorta sample where SHG is shown in
blue, TPEF is shown in green, and CARS at 2850 cm-1 is shown in red. (b) Grayscale image of the
2850 cm-1 CARS channel shown as red in (a). The spectra on the right are representative spectra
from two individual bright (tissue) and dark (background) pixels in the image. Scale Bar: 30 µm
Figure 3. Optical set-up of the multimodal/hyperspectral CARS microscopy system. A 60-fs laser
beam centered at 800nm is split into two beams, one beam becomes the pump/probe (at 800nm
and the other beam generates a supercontinuum using a photonic crystal fiber. The red part of the
supercontinuum (~950-1150nm) becomes the “Stokes” beam. The two beams are chirp-matched
using high dispersion SF6 glass and they are overlapped in time and space. Spectral scanning is
done by overlapping the pump with different portions of the “Stokes” beam by delaying the arrival
time of the pump/probe beam using a high-resolution linear stage. The two beams are sent to the
microscope where high speed galvo mirrors raster-scan the beam over the sample.
Figure 4. Principal component analysis of the hyperspectral CARS sample image. (a) Cumulative
variance plot shows that only two principal components (PCs) are needed to cover ~90% of the
variance in the data set. No appreciable increase in the cumulative variance is observed after PC2 as
shown for PC3 to PC6. (b) Score plot of the first two principal components (PC1 and PC2). Each
point on the plot corresponds to one pixel in the image. (c) The color assignments on the retrieved
PCA image depends on which quadrant the pixel object is located on in the score plot in (b). Scale
Bar: 30 µm
Figure 5. Vertex component analysis of atherosclerotic rabbit aorta tissue sample. (a) Retrieved
VCA image with three endmembers. (b) Retrieved VCA image with four endmembers. (c,d)
Endmember spectra for three- and four-endmember VCA, respectively. Scale Bar: 30 µm