SUPPLEMENTAL MATERIAL
Supplemental Methods
Animal model of TCFA and histology
One female ApoE-/- mouse was housed in the animal unit at Imperial College London. Animal
care and all procedures complied with the Animals Act 1986 and were approved by the
Home Office, UK. The mouse was initiated on a high-fat Western diet (Lillico Biotech, UK) at
the age of 11 weeks and, 2 weeks later, a blood flow-modifying cuff (Promolding, Rijswijk,
The Netherlands) was surgically placed around the left carotid artery. The cuff tapers from
500 m at the base to 250 m at the throat and creates a gradual artery stenosis with a
maximum of ~75% by area, leading to three distinct regions of perturbed flow characterized
by low wall shear stress (WSS) upstream, high WSS within, and low, oscillatory WSS
(characterized by vortices) downstream of the cuff. Within 9 weeks of instrumentation, the
cuff caused the development of TCFA in the segment upstream of the cuff, fibrous cap
atheroma in the segment downstream of the cuff, and very little plaque within the cuff, as
previously reported [1]. In this study, we focused on the TCFA in the upstream region.
At 9 weeks, the mouse was sacrificed and the carotid arteries were harvested. Arteries were
embedded in OCT and serially sectioned frozen at 8 µm intervals over the entire TCFA
region upstream of the cuff. Sections were collected using an alternating methodology to
allow assessment of the distribution of lipid (oil-red-O), collagen (picrosirius red), and
stiffness (Brillouin shift) in neighbouring sections (i.e., oil-red-O and collagen staining were
performed on sections that were 22.40±14.31 µm and 30.4±14.31 µm apart, respectively,
from sections used for Brillouin measurements). Oil-red-O staining was done in 0.5% Oilred-O solution in Propylene glycol (Sigma Aldrich, UK) and a nuclear counterstain was done
using Mayer’s Hemotoxylin (Sigma Aldrich, UK). After staining, all histology sections were
imaged (MicroBeam 4.5 Pro laser capture microscope; Carl Zeiss, UK) at 10x magnification.
Picrosirius red staining was done by immersing sections in Celestin Blue (Solmedia, UK) for
15 seconds, Harris Haematoxylin (Solmedia, UK) for 15 seconds, and picrosirius red (Sigma
Aldrich, UK) for 1 hour with a tap water rinse between each step. Samples were then
washed in acetic acid water, rinsed in tap water, and dehydrated through an ethanol series
(70, 90, 100, and 100%). Sections were imaged using a light microscope with a polarizing
filter at 10x magnification.
Brillouin microscopy
Spontaneous Brillouin scattering, first reported in 1922 [2], is a weak inelastic scattering process
arising from the interaction of light with thermal acoustic waves (acoustic phonons) propagating
at hypersound velocity in a medium. The spectrum of the scattered light contains the
illumination frequency (Rayleigh peak) and two other frequencies, one blue- and one red-shifted
with respect to the Rayleigh peak. The two peaks on either side of the Rayleigh peak and equal
spectral distance (or shift) away from that, are referred to as the Brillouin peaks. The frequency
shift
of the Brillouin scattered light is given by
,
where
(1)
is the frequency of the illumination, c is the speed of light, n is the (local) refractive
index, θ is the scattering angle (measured between the incident wave vector and the wave
vector of the scattered light) and V is the hypersound velocity. Note that this equation either
applies in general to isotropic media or specifically to a particular direction in anisotropic
media.
In isotropic media, the real part of the longitudinal modulus, also referred to as the Brillouin
or longitudinal storage modulus M’, is given as
,
(2)
where ρ is the material density. In anisotropic media there is a separate M’ in each direction
corresponding to direction-dependent hypersound velocities. If an anisotropic sample with
stiffness variations smaller than the optical resolution is measured in a Brillouin microscope,
the resulting Brillouin shift will be due to the mean hypersound velocity within the probe
volume. The width of the Brillouin peak on the other hand is related to the imaginary part of
the longitudinal modulus, the so-called loss modulus. The simultaneous knowledge of
storage and loss moduli together provides complete stiffness information of the sample at
each pixel at the frequency of hypersound velocity.
A recent study [3] found a linear relationship between the Brillouin modulus and Young’s
modulus for a limited range of moduli. More precisely, Scarcelli et al. [3] used small volumes
of fresh porcine and bovine eye lens tissue and carried out rheometer measurements to
obtain Young’s moduli of elasticity for these samples. Subsequently, they carried out low
resolution Brillouin microscope imaging of both samples to obtain the Brillouin frequency
shift. The average of these values was then used to calculate M’ using Eqs. (1) and (2),
which assume the knowledge of the refractive index, n, material density, ρ, and the
scattering angle, θ. Whereas the last of the three parameters can be readily estimated in the
case of low resolution measurements from the optical configuration of the microscope, the
refractive index and material density are more difficult to measure. Scarcelli et al. elected to
estimate these parameters; an approach that can be clearly justified when larger volumes of
the sample are considered. Averaging over large volumes becomes particularly important in
the case of anisotropic eye lenses because their direction dependent material properties
would potentially yield very misleading data should the measurements involve small
volumes. The authors also point out that, in general, moduli of elasticity depend on the
frequency of the mechanical stimulus and so a significant difference is expected between
moduli obtained by static rheometry, dynamic rheometry and Brillouin spectroscopy.
Returning now to our present work, high resolution Brillouin microscopy provides information
on the frequency shift in the following way. Due to the high numerical aperture (NA)
illumination and detection, the scattering angle encompasses θ = 0 – 57° angle range, which
causes the Brillouin peak to broaden and shift position [6]. This is not a problem in terms of
the measurement accuracy because the effect is well understood; therefore, when
significant, in some cases it can be calibrated out. Furthermore, the volume of the focused
light (probe volume) that illuminates the sample is 0.435 µm3 so the measured frequency
shift at each pixel is due to the average hypersound velocity within the probe volume. This
again does not invalidate the data as long as it is clearly understood that, according to Eq.
(1), pixel to pixel variations in the measured Brillouin frequency shift, may arise due to
changes in either or both the average hypersound velocity and the refractive index.
Therefore, in order to be able to calculate the hypersound velocity from the measured
Brillouin shift one needs to determine the average reflective index within the probe volume.
To appreciate how much error the assumption of uniform refractive index introduces,
consider that the refractive index of the artery wall varies between 1.39 (intima), 1.38
(media), and 1.36 (adventitia) [7] whereas the refractive index of lipid within the plaque is
1.42 [8]. Therefore, since Eq. (1) reveals a linear dependence of the Brillouin shift on the
refractive index; the maximum error one introduces within the artery wall is ~1.5% and
between the artery wall and the lipid is ~4%. This error is at the detection limit of our system.
A more significant problem arises when one is required to calculate the Brillouin modulus
from the frequency shift. This calculation requires the knowledge of the material density
within the probe volume, which is a quantity we have even less knowledge of than the
refractive index. The other disadvantage of using elasticity moduli values to display the
results of Brillouin microscope measurements is that the dimension of Brillouin modulus
values (Pa) would encourage direct comparisons with other methods (e.g. AFM, optical
elastography, microrheology, etc.). We have pointed out before, in agreement with Scarcelli
et al. [3], that direct comparisons cannot be related to the elastic moduli obtained from
different methods in a simple manner, particularly for anisotropic materials.
Therefore, for purposes of this study, it is more reasonable to infer the stiffness obtained
from the Brillouin microscopy data directly from the Brillouin frequency shift, instead of the
hypersound velocity or Brillouin modulus (which we showed in our original submission).
Future work, including the combined use of refractive index measurements and
micromechanical simulations, will permit the calculation of an elastic modulus to allow
computation of plaque stress distributions, which is the primary method of determining
plaque vulnerability.
To obtain the Brillouin frequency shift, a custom confocal Brillouin microscope was designed
and built to acquire high spatial resolution images. Supplemental Figure 1 shows the
diagram of the optical system. The light emitted by a Cobolt Jive DPSS single longitudinal
mode laser (λ=561 nm) was focused on the sample by an oil-immersion microscope
objective lens (100x, NA=1.3). The theoretical optical resolution values associated with our
wavelength and numerical aperture are 300 nm (transversal) and 1.54 µm (axial). The light
scattered by the sample was collected by the same lens and it was used in conjunction with
another, lower NA lens to couple the light from the probe volume into a single mode optical
fibre. The light exiting the fibre was collimated and subsequently incident upon the
spectrometer. Spectral analysis was performed by means of a pair of crossed Virtually
Imaged Phased Array (VIPA), resulting in an overall extinction of 60dB. The VIPA is a
customised Fabry-Perot etalon that incorporates an anti-reflection (AR) coated entrance
window to minimise optical losses [4,5]. The spectra were captured by an Andor Neo
sCMOS camera set to 0.2s data acquisition time. Lorentzian function fitting was performed
on the row spectra to aid the accuracy of Brillouin peak localisation. The Brillouin spectrum
of water was used as a reference (
GHz) to permit calibration of the spectrometer.
The sample was raster scanned by a Prior H117 motorised XY stage having 40nm step size.
Correlation analysis
The Brillouin microscope created a point-to-point Brillouin frequency shift (a measure of
stiffness) map for each imaged vessel section. Each shift map was imported into a custom
Matlab (version R2012a, Mathworks Inc., USA) program to segment the lumen, internal
elastic lamina (IEL), and external elastic lamina (EEL). The average frequency shift could
then be computed for each component of the vessel section, including the intima (or plaque
region) and media (also referred to as wall, which is the space between the IEL and EEL; for
control sections the intima could not be delineated, so the wall was the space between the
lumen and EEL). In addition, the region within each Brillouin image between the lumen and
EEL was broken into a grid of 30 equidistant points circumferentially and 20 equidistant
points radially and the mean Brillouin shift was assigned to each grid point based on
proximity (i.e., each grid point “represented” a local region or area within each vessel section
and the mean Brillouin shift within that local region was assigned to the grid point).
Histology sections were analysed similarly, via the following process (see Supplemental
Figure 2 for a summary). First, each digitized histology section was also segmented to
delineate the lumen, IEL, and EEL contours and the lipid stain was identified via a threshold
(based on inspection of both the instrumented and control sections, which was then kept
constant over all sections) using commercial software (Clemex Technologies, Canada). The
contour and stain data were discretized (i.e., broken into small points) so that the centroid
and area (area was only outputted for stain data) associated with each point could be
exported to an XLS file. These data were then imported into Matlab and, identical to the
discretization for the Brillouin shift map described above, the region between the lumen and
EEL was broken into a grid of 30 equidistant points circumferentially and 20 equidistant
points radially. Next, the stain data (x-, y- coordinates of each centroid and area in µm2) was
assigned to each grid point based on proximity and stain areas were summed at each grid
point. Since each grid point “represented” a local region or area of the vessel cross-section,
the summed stain at a given grid point could be scaled by the total area represented by that
point, which gives the stain value over the range from 0 (meaning no stain area at the given
grid point) to 1 (100% of the area at a given grid point is stained). This approach was taken
for both the lipid and collagen stains.
The identical approach to discretizing the stain and Brillouin maps facilitated their coregistration in the form of pairing the Brillouin shift map to each of the stains, lipid and
collagen, respectively, which required only one additional step. Two markers were selected
that represented the same points on each of the two images of the shift-stain pairing
(identified based on comparable morphology of the sections), which were used to rotate the
Brillouin image with respect to the histology image to complete the co-registration. Because
the histology and Brillouin images were not identical, only neighbouring, the stiffness and
lipid stain area values were averaged circumferentially. This led to 20 values for each metric
(Brillouin shift, lipid, and collagen), wherein each value per metric represented each of the 20
equidistantly spaced radial points of the grid. A Spearman’s correlation analysis was then
performed to examine the relationship between stain area and Brillouin frequency shift along
the radius of each image pairing.
Supplemental Figures and Legends
Supplemental Figure 1. Diagram of the confocal Brillouin microscope. The laser beam is
focused by an oil-immersion objective (100x) into the sample. The scattered light is delivered
by a single mode fibre to the 2-stage VIPA spectrometer. The water acts as reference for
calibration before measurements.
Supplemental Figure 2. Steps used to develop a quantitative spatial map of each stain. (A)
Histology images were imported into Clemex and the lumen, IEL, and EEL were manually
segmented. (B) A threshold was then applied to the image to identify regions of stain (lipid is
shown). (C) The custom script written in Clemex then discretized the stain area (i.e., broke
the stain into very small regions or points). The program then outputted the centroid and
area (µm2) associated with each stain point, as well as the contour points. (D) The points
associated with the lumen and EEL contours (defined now by x-, y- coordinates of each
centroid; given by red for EEL and purple for lumen) and stain data (defined by centroids and
areas; given by magenta points) were then imported into Matlab. (E) A custom Matlab
program was used to create a grid of 30 equidistant points circumferentially and 20
equidistant points radially. The stain areas were then assigned to each point based on
proximity and summed. Since each discretized grid point of the vessel cross-section
represented a specific area of that cross-section, the summed stain area could be scaled by
the total area “represented” by each grid point to address how much of the vessel section in
that local region had stain (from 0 – no stain to 1 – 100% of the area was stained).
Supplemental References
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