# Polarimetric imaging of the human brain to determine the orientation and
degree of alignment of nerve fiber bundles

Arushi Jain1  Leonie Ulrich1  Michael Jaeger1  Philippe Schucht2  Martin
Frenz1,* and H. Günhan Akarcay1  *Corresponding author:
<EMAIL_ADDRESS>1Biomedical Photonics Department, Institute of
Applied Physics, University of Bern, Sidlerstrasse 5 CH-3012 Bern, Switzerland
2Department of Neurosurgery, University hospital Bern, Freiburgstrasse 16
CH-3010 Bern, Switzerland

###### Abstract

More children and adults under the age of 40 die of brain tumor than from any
other cancer. Brain surgery constitutes the first and decisive step for the
treatment of such tumors. It is extremely crucial to achieve complete tumor
resection during surgery, however, this is a highly challenging task, as it is
very difficult to visually differentiate tumorous cells from the surrounding
healthy white matter. The nerve fiber bundles constitutive of the white matter
are organized in such a way that they exhibit a certain degree of structural
anisotropy and birefringence. The birefringence exhibited by such aligned
fibrous tissue is known to be extremely sensitive to small pathological
alterations. Indeed, highly aligned anisotropic fibers exhibit higher
birefringence than structures with weaker alignment and anisotropy, such as
cancerous tissue.

In this study, we performed experiments on thick coronal slices of a healthy
human brain to explore the possibility of (i) measuring, with a polarimetric
microscope (employed in the backscattering geometry to facilitate non-invasive
diagnostics), the birefringence exhibited by the white matter and (ii)
relating the measured birefringence to the fiber orientation and the degree of
alignment. This is done by analyzing the spatial distribution of the degree of
polarization of the backscattered light and its variation with the
polarization state of the probing beam.

We demonstrate that polarimetry can be used to reliably distinguish between
white and gray matter in the brain, which might help to intraoperatively
delineate unstructured tumorous tissue and well organized healthy brain
tissue. In addition, we show that our technique is able to sensitively
reconstruct the local mean nerve fiber orientation in the brain, which can
help to guide tumor resections by identifying vital nerve fiber trajectories
thereby improving the outcome of the brain surgery.

††journal: oe

##  1 Introduction

Cancer is a global burden that leads to public health and economic problems
and ranks as the first or second leading cause of premature death [1]. Brain
tumors, in particular the malignant ones, were responsible for 238’000 new
cases in 2008 worldwide [2, 3]. The primary treatment for a brain tumor is
surgery followed by adjuvant chemo or radio therapy. Gross total resection,
i.e., removal the bulk of cancer cells, is paramount for an improved
prognosis. Hence, the accuracy of the estimation of the tumor’s borders
carries heavy consequences for the patients: on one hand, subtotal resection
leads to increased risk of recurrence and shorter life expectancy [4, 5, 6]
and, on the other hand, if healthy tissue is removed as a result of gross
resection, this might irrevocably damage the brain, leading to irreversible
disabilities and a decreased quality of life which again might decrease life
expectancy [7]. The accurate resection of the malignant tumor is also a
fundamental prerequisite for efficient adjuvant therapy [8, 9]. The prime
difficulty resides in identifying clear borders to the tumorous cells to
define adequate safety margins given the infiltrative nature of most brain
tumor types [10, 11].

Current intraoperative modalities to delineate the tumor include visualization
tools such as image guided neuronavigation, magnetic resonance imaging,
computed tomography, or ultrasound [12, 13, 14, 15], fluorescence guided
techniques [16, 17, 18, 19], and histopathology. Unfortunately, these
modalities, having significantly improved tumor detection are still unable to
reliably differentiate cancerous from healthy tissue [20, 21, 22, 23].

Polarimetric light imaging is a promising alternative to aforementioned
techniques [24, 25, 26] . White matter in the mammalian brain primarily
comprises of nerve fiber bundles [27] that exhibit a certain degree of
structural anisotropy and anisotropy in dielectric response [28]. These
effects are coupled and manifest themselves via optical birefringence [29].
Consequently, polarimetric light imaging has been used to reconstruct three-
dimensional architecture of nerve fiber bundles and to map the nerve fibers
orientations in and out of the plane of histological sections of a human brain
[30, 31, 32, 33, 34, 35, 36]. Imaging the nerve fibers and their connectivity
is also of great interest to construct the human connectome in order to
unravel the architecture and connectivity of the nerve fiber bundles [37].

Conversely, the polarimetric response of brain tissue can be used to detect
disease-related derangement of the white matter’s structural integrity. It
has, for example, been shown that the white matter tracts in children (six
months) affected by autism spectrum disorder show aberrant development [38].
Similarly, the anisotropy is observed to be weaker in a cancerous or scar
tissue than in health tissue [39, 40], allowing to observe even small
alterations via polarimetry [41, 42]. Hence, there is potential for
polarimetric imaging to be used for non-invasive, non-contact, and real-time
intra-operative cancer delineation.

As a first step towards this goal, we focus in this study on demonstrating
that backscattering polarimetric microscopy is sensitive to detect structural
differences in nerve fiber architecture in the human brain. The methodology
follows the one presented in [43, 44], where the spatial distribution of
polarization of diffusely backscattered light is analyzed as a function of
input polarization of a weakly focused probing beam. This allows us to assess
the samples’ structural anisotropy and thus give an indication of its degree
of alignment. We proved that the degree of linear polarization can be used as
a measure for determining the degree of alignment of fibrous materials.
Although our final goal is to distinguish between tumorous tissue and healthy
white matter, here, our aim is to test the methodology on non-tumorous
formalin fixed (from now referred to as healthy) brain tissue. Firstly, we
demonstrate the ability to distinguish between the highly aligned nerve fiber
architecture in white matter and the low degree of alignment in gray matter,
two tissues where the clear visual discriminability serves as ground truth.
Secondly, our results indicate that our technique is even able to capture
subtle variations of degree of alignment and fiber orientation within the
white matter.

##  2 Materials and methods

Figure 1: (a) Photograph of a coronal cross section of a healthy human brain
fixed in $4\%$ formaldehyde solution. The regions marked in different colors
were probed in this study. The medial side of the brain was aligned parallel
to the x-axis in the output coordinate system ($\sum_{out}$). (b) shows zoomed
in images of the regions marked as A, B, C and D in (a). The red points
illustrate the illumination spots of the probing beam (measurement points
$\textbf{r}_{i}$). GM: Gray Matter, CC: Corpus Callosum, EC: External Capsule,
IC: Internal Capsule and PCG: Pre-Central Gyrus.

###  2.1 Brain sample

Two types of tissues can visually easily be distinguished within the brain,
i.e., gray matter and white matter (see Fig. 1(a)). The gray matter, also
called cortex, constitutes the surface of the brain and is home to the cell
bodies of the neurons. Multiple folds, called gyri, increase the surface of
the brain. The white matter below the gray matter is made up of nerve fibers
(axons) through which different neurons interact with each other. Nerve fibers
that reach neurons in neighboring gyri are called U-fibers. Nerve fibers that
reach neurons further away on the same hemisphere of the brain are called
association fibers and those connecting the two hemispheres of the brain are
called commissural fibers. Finally, projection fibers link the white matter to
the spinal cord. For better electric conductivity along the fibers, most nerve
fibers are isolated through sheaths of myelin, which are responsible for the
white color of the white matter and for the birefringent properties of the
nerve fibers [45].

Fig. 1(a) shows a coronal section of a healthy human brain (anonymous donor).
The sample was obtained during autopsy and was fixed in neutral buffer
formalin ($4\%$ formeldehyde) solution. For our investigation, we have
selected distinct areas within this section: A, B, C and D. The corpus
callosum (region C) consists of commissural fibers that connect the left and
right hemisphere of the brain. The corpus callosum is the largest fiber tract
system in the brain, along its axis all the fibers are aligned. The external
capsule, a thin elongated structure (region B), consists of projection fibers
connecting the frontal lobe and the spinal cord, as well as to a lesser degree
of association fibers that interconnect the frontal and the parietal cortex.
Inside the external capsule, a distinct orientation of fibers along the axis
of this elongated structure is thus found. Whereas the corpus callosum and the
external capsule each represent a well-aligned fiber system, the white matter
inside the gyri contains connections to various parts of the brain and thus a
mixture of U-fibers, association, commissurial and projection fibers. This
results in fibers aligned at different depths in different directions and
often over several levels with a mean fiber orientation towards the center of
the brain [46]. The superior frontal gyrus (region D) was chosen to showcase
this situation. Whereas region B to D were chosen to allow the investigation
of distinctive features of fiber alignment in white matter, we additionally
selected region A to investigate the response of gray matter.

Figure 2: (a) Schematic drawing (not to scale) of the polarimetric imaging
setup used to probe the brain sample in the backscattering geometry. This
instrument has two arms: an illumination and a detection arm containing
polarization state generator (PSG) and polarization state analyzer (PSA),
respectively. LC, L1, and L2 denote lenses. LCR are liquid crystal retarders
and LP are linear polarizers. The tissue sample was probed at
$\lambda=700\,nm$ with a focused beam. The backscattered intensity
distribution is recorded by a CCD camera. $\sum_{lab}$ denotes the laboratory
frame. (b) Schematic representation of the orientation of the right-handed
coordinate systems involved in the experimental setup, relative to the brain
sample. The input polarization state is defined in the input coordinate system
($\sum_{in}$). The detection frame $\sum_{out}$ attached to the CCD chip
coincides with $\sum_{lab}$. For the radial analysis carried out in this
study, each point on the probed surface is defined by the polar coordinates
$(\rho,\phi)$, where the probing beam was focussed at
$\textbf{r}(\rho=0,\phi=0)$.

###  2.2 The polarimetric microscope

The polarimeteric microscope used to probe the coronal section of the healthy
human brain is described in detail [43, 44] and was slightly adapted for this
study. An objective lens (L2) of focal length $f=30$ mm (NA = 0.13) was used
to focus the polarized illumination beam onto the tissue surface. The beam’s
spot radius ($1/e^{2}$) was measured to be $43$ $\mu$m. The backscattered
light was guided through the two-lens system composed of the objective lens L2
and a second lens L1 (focal length $f=100$ mm). A CCD chip (ptGray
grasshopper, 16bit, $2448\times 2048$ pixels) positioned at the end of the
detection arm was used to image (with a magnification of $\sim 3.1$) the
spatial distribution of the backscattered light from the sample surface (field
of view 500 x 500 $\mu$$m^{2}$). All measurements presented were performed at
$\lambda=$700 nm. A computerized scanning stage (H101P2BX ProScan stage
operated via a V31XYZE controller, both from PRIOR Scientific) was used to
scan the sample in $x,y-$direction.

###  2.3 Measurement procedure

The tissue sample was taken out from the $4\%$ formaldehyde solution and
placed on a Petri dish. It was then positioned under the polarimetric
microscope such that the medial part of the brain was aligned parallel to the
$x-$axis in the lab coordinate system ($\sum_{lab}$), as depicted in Fig. 1.
To ascertain a consistent spatial registration of different measurement
points, all the measurements were performed with the same placement of the
sample. The backscattered intensity distribution, recorded for different pairs
of illumination and detection states, was averaged 10 times for noise
reduction. For each measurement point, speckle noise was further reduced by
repeating the measurement at four different beam positions located on the
corners of a $5\,\mu m$ square region and again averaging the results. In
addition to this, the background noise/dark current of the CCD was subtracted.
For each region (A to D) on the brain sample, we probed various points
$\textbf{r}_{i}$. For visualization of the position of the measurement points
relative to the anatomy of the brain sample, we overlay the points onto the
widefield images of the tissue surface taken using white light illumination
from the polarimetric microscope.

###  2.4 Analysis of the polarimetric data

The methodology applied in this study is discussed in detail in [43, 44]. In
[44], we analyzed the polarimetric response from fibrous membranes
(electrospun PVDFhfp scaffold) with varying degree of alignment to understand
how the structural anisotropy manifests itself in the polarimetric response.
More precisely, we analyzed the backscattered Stokes vector $\vec{S}$, from
which we calculated the four polarization ellipse parameters (PEPs;
orientation, ellipticity, helicity and degree of polarization). This results
in spatially resolved maps of PEPs, which are conveniently defined in a polar
coordinate system $(\rho,\phi)$, where $\rho$ is the distance from the probing
beam center, and $\phi$ is the angle relative to the x-axis of the output
coordinate system. Among the various PEPs, the spatial distribution of the
degree of linear polarization (DOLP) $\Pi_{L}(\rho,\phi)$ gives a most
intuitive understanding of the fibrous samples’ degree of alignment. To
simplify the analysis, we performed a radial averaging of the
$\Pi_{L}(\rho,\phi)$-image, resulting in
$\left\langle\Pi_{L}(\phi)\right\rangle_{\rho}$. By analyzing the dependence
of $\phi_{max}$ with respect to the input stokes vector $\vec{S}_{in}$, a
correlation between anisotropy and birefringence can be established.
$\phi_{max}$ is defined as the direction $\phi$ for which maximum linear
states are found in $\left\langle\Pi_{L}(\phi)\right\rangle_{\rho}$. In
addition, the dependence of the peak value of
$\left\langle\Pi_{L}(\phi=\phi_{max})\right\rangle_{\rho}$ with respect to the
orientation of $\vec{S}_{in}$ is also analyzed. To determine $\phi_{max}$ and
$\left\langle\Pi_{L}(\phi_{max})\right\rangle_{\rho}$, we fit a Gaussian
model. To estimate the mean alignment direction of the fibers in the
membranes, we analyze the orientation $\psi(\rho,\phi)$ parameter in the PEPs
[44], i.e. the orientation of the major axis of the polarization ellipse.

##  3 Results and discussion

Figure 3: Exemplary result for gray matter, point $\textbf{r}_{1}$ in region
A. (a) The spatial distribution of the $\Pi_{L}(\rho,\phi)$\- image for the
input polarization state depicted in red (in $S_{in}=x$), is shown in the
output coordinate system ($\sum_{out}$). The red circle at the center of the
image represents the focal spot size and position of the probing beam. (b) The
radial analysis of the $\Pi_{L}(\rho,\phi)$\- image, for the input state in
red (in $\sum_{in}$, $S_{in}=0$). Video 1 (supplementary work) shows the
$\Pi_{L}(\rho,\phi)$\- image and video 2 (supplementary work) illustrates the
radial analysis for different input polarization state ($S_{in}=0\,to\,\pi$).
(c) Azimuthal angle $\phi_{max}$ at which the maximum of
$\left\langle\Pi_{L}(\phi)\right\rangle_{\rho}$ was recorded for different
orientations (between $\pi/2$ and $-\pi/2$ in $\Sigma_{out}$) of the linear
polarization $\vec{S}_{in}$ of the probing beam. (d) Peak value of
$\left\langle\Pi_{L}(\phi)\right\rangle_{\rho}$ recorded at $\phi_{max}$ for
different orientations (between $0$ and $\pi$ in $\Sigma_{in}$) of the linear
polarization $\vec{S}_{in}$ of the probing beam ($\vec{S}_{in}$ is given in
different coordinate systems for better representation of the outcomes).
$\phi_{max}$ and $\left\langle\Pi_{L}(\phi=\phi_{max})\right\rangle_{\rho}$
values are left blank for states $\vec{S}_{in}$ where no peak was identifiable
in the radial analysis of the $\Pi_{L}(\rho,\phi)$-images. For reference, we
performed the same radial analysis on measurements collected from colloidal
suspensions [43] (dashed black lines), to showcase quasi-perfect rotational
symmetry. Figure 4: Exemplary result for white matter, point $\textbf{r}_{1}$
in region C. (a) The spatial distribution of the $\Pi_{L}(\rho,\phi)$\- image
for input polarization state depicted in red (in $\sum_{in}$, $S_{in}=0$), is
shown in the output coordinate system $\sum_{out}$. The red circle at the
center of the image represents the focal spot size and position of the probing
beam. (b) The radial analysis of the $\Pi_{L}(\rho,\phi)$\- image, for the
input state in red. Video 3 (supplementary work) shows the
$\Pi_{L}(\rho,\phi)$\- image and video 4 (supplementary work) illustrates the
radial analysis for different input polarization state ($S_{in}=0\,to\,\pi$).
(c) Azimuthal angle $\phi_{max}$ (dotted line)at which the maximum of
$\left\langle\Pi_{L}(\phi)\right\rangle_{\rho}$ was recorded for different
orientations (between $\pi/2$ and $-\pi/2$ in $\Sigma_{out}$) of the linear
polarization $\vec{S}_{in}$ of the probing beam. (d) Peak value of
$\left\langle\Pi_{L}(\phi)\right\rangle_{\rho}$ (dotted line)recorded at
$\phi_{max}$ for different orientations (between $0$ and $\pi$ in
$\Sigma_{in}$) of the linear polarization $\vec{S}_{in}$ of the probing beam
($\vec{S}_{in}$ is given in different coordinate systems for better
representation of the outcomes). $\phi_{max}$ and
$\left\langle\Pi_{L}(\phi=\phi_{max})\right\rangle_{\rho}$ values are left
blank for states $\vec{S}_{in}$ where no peak was identifiable in the radial
analysis of the $\Pi_{L}(\rho,\phi)$-images. For anisotropic sample the peak
depicting the preservation of maximum linear states is
$\vec{S}_{in}=\vec{S}_{max}$.

###  3.1 Polarimetric response for gray and white matter

The key difference between gray and white matter of the brain is that gray
matter majoritarily comprises of nucleon cells while white matter comprises of
nerve fibers. First we analyzed the polarimetric response of two exemplarly
points representing gray (point $\textbf{r}_{1}$, region A) and white matter
(point $\textbf{r}_{1}$, region C), respectively.

Fig. 3 shows the results for point $\textbf{r}_{1}$, region A (gray matter).
In Fig. 3(a) we see the $\Pi_{L}(\rho,\phi)$\- image recorded for the input
polarization state in red (in input coordinate system $\sum_{in}$), and Fig.
3(b) shows its respective radial analysis and Gaussian fit. The response is
isotropic, i.e., observed as symmetry with respect to rotation of the input
polarization, termed "rotational symmetry" in the remainder of this study.
This rotational symmetry becomes evident in the animation depicting the
spatial distribution of the $\Pi_{L}(\rho,\phi)$\- image for different
polarization of the probing beam ($\sum_{in}$) (see video 1, supplementary
work). The symmetry observed in video 1 is quantified in Fig. 3(c) and (d),
where the azimuthal direction $\phi_{max}$ along which the pattern is
stretched depends on the polarization state of the probing beam
$\vec{S}_{in}$. The strength of linear states depicts a quasi-flat response
with respect to $\vec{S}_{in}$ which means that the depolarization does not
depend on the orientation of the imput state. The values are left blank for
polarization probing states $\vec{S}_{in}$ where no peak was identifiable. For
comparison, the response from a colloidal suspension (175 nm radius
polystyrene spheres diluted in water, see [43]) showing a perfect rotational
symmetry has been plotted as dashed black lines in Fig. 3(c) and (d).

Fig. 4 shows the analogue results for white matter (point $\textbf{r}_{1}$,
region C). In contrast to gray matter no rotational symmetry can be observed,
which indicates anisotropy (see video 3, supplementary work). Fig. 4(c)
provides a quantitative visualization of the anisotropic nature of the tissue,
i.e., the azimuthal direction $\phi_{max}$ along which the patterns in the
$\Pi_{L}(\rho,\phi)$-images are stretched does not significantly depend on the
orientation of the probing beam’s polarization. Furthermore, the linearity of
the probing beam’s polarization state $\vec{S}_{in}$ is preserved
predominantly for input states with orientations of $\vec{S}_{in}$ that are
parallel and perpendicular to $\phi_{max}$. In [44] we observed the same co-
occurrence of rotational anisotropy and preservation of linear states in
aligned PVDFhfp electrospun fibrous membranes and argued that this behaviour
reflects the uniaxial birefringence of the material. For the brain sample, we
observe a distinctive peak around a specific input state $\vec{S}_{in}$,
defined as $\vec{S}_{max}$, where maximum linear polarization states are
preserved (Fig 4(d)). This allows us to define the mean orientation of the
nerve fibers.

Figure 5: Summary of results from all points in region A and region C. (a,c)
azimuthal angle $\phi_{max}$ at which the maximum of
$\left\langle\Pi_{L}(\phi)\right\rangle_{\rho}$ was recorded for different
orientations (between $\pi/2$ and $-\pi/2$ in $\Sigma_{out}$) of the linear
polarization $\vec{S}_{in}$ of the probing beam. (b,d) peak value of
$\left\langle\Pi_{L}(\phi)\right\rangle_{\rho}$ recorded at $\phi_{max}$ for
different orientations (between $0$ and $\pi$ in $\Sigma_{in}$) of the linear
polarization $\vec{S}_{in}$ of the probing beam ($\vec{S}_{in}$ is given in
different coordinate systems for better representation of the outcomes).
$\phi_{max}$ and $\left\langle\Pi_{L}(\phi=\phi_{max})\right\rangle_{\rho}$
values are left blank for states $\vec{S}_{in}$ where no peak was identifiable
in the radial analysis of the $\Pi_{L}(\rho,\phi)$-images. For anisotropic
samples, $\vec{S}_{in}=\vec{S}_{max}$ is the input polarization state for
which maximum linear output states are obtained (see (d). As a reference of
rotational symmetry, the same radial analysis is shown for a colloidal
suspension [43] (dashed black lines).

Fig. 5 shows the responses for various different measurement points
($\textbf{r}_{i}$) in regions A and C, respectively. These results showcase
the reproducibility of rotational symmetry in gray matter (i.e. all the points
in region A and point $r_{7}$ in region C), and anisotropy in white matter
(i.e. for points $\textbf{r}_{i}$, for i=1…6 in region C).

Similarly, for regions D and B, the resulting curves for different measurement
points are presented in Fig. 6.

In all points in all areas, the results are akin to those of the electrospun
PVDFhfp scaffolds and colloidal suspensions [44]. In the gray matter, where a
low degree of alignment is expected due to the quasi-random intermixing of
cell bodies, dendrites, and nerve fibers, the polarimetric response is that of
an isotropically scattering medium. In the white matter, where a significant
degree of alignment is expected due to the alignment of nerve fibers, the
polarimetric response resembles that of a uniaxially birefringent medium.

Figure 6: Summary of results from all points in region D and region B. (a,c)
azimuthal angle $\phi_{max}$ at which the maximum of
$\left\langle\Pi_{L}(\phi)\right\rangle_{\rho}$ was recorded for different
orientations (between $\pi/2$ and $-\pi/2$ in $\Sigma_{out}$) of the linear
polarization $\vec{S}_{in}$ of the probing beam . (b,d) peak value of
$\left\langle\Pi_{L}(\phi)\right\rangle_{\rho}$ recorded at $\phi_{max}$ for
different orientations (between $0$ and $\pi$ in $\Sigma_{in}$) of the linear
polarization $\vec{S}_{in}$ of the probing beam ($\vec{S}_{in}$ is given in
different coordinate systems for better representation of the outcomes).
$\phi_{max}$ and $\left\langle\Pi_{L}(\phi=\phi_{max})\right\rangle_{\rho}$
values are left blank for states $\vec{S}_{in}$ where no peak was identifiable
in the radial analysis of the $\Pi_{L}(\rho,\phi)$-images. For anisotropic
samples, $\vec{S}_{in}=\vec{S}_{max}$ is the input polarization state for
which maximum linear output states are obtained. As a reference of rotational
symmetry, the same radial analysis is shown for a colloidal suspension [43]
(dashed black lines).

###  3.2 Estimating the mean alignment direction and degree of alignment of
nerve fibers

In our previous study on electrospun PVDFhfp scaffolds [44] we could show that
in samples that exhibit a certain degree of alignment linear states are
maximally preserved for input polarization $\vec{S}_{in}$ parallel and
perpendicular to the mean fiber alignment direction, and that the direction
$\phi_{max}$ (along which the $\Pi_{L}(\rho,\phi)$-image is stretched) is
perpendicular to the fiber orientation. In the present study, where the mean
alignment direction of nerve fibers in the white matter is a priori unknown,
we take the direction of the probing state $\vec{S}_{max}$ (which is roughly
perpendicular to $\phi_{max}$) as a proxy for the mean alignment direction.
Then, in order to refine this quantification, we analyze the orientation
parameter $\psi(\rho,\phi)$, i.e. the PEP which describes the orientation of
the major axis of the polarization ellipse. The mean alignment direction is
estimated as the mean orientation parameter over $\rho$ along
$\phi=\phi_{max}$.

The curves in Fig. 5(a,c) and Fig. 6(a,c) provide a quantitative indicator for
the degree of alignment, but their interpretation so far relies on visual
inspection of the slope of the curves. Thereby, a slope near -1 indicates a
low degree of alignment, while a slope near 0 indicates a high degree of
aligment [44]. For a quantitative assessment of the slope we calculated the
derivative at every input state and took the median of its distribution, which
we define as the slope parameter $\mathscr{m}$. In Table 1 the values of
$\mathscr{m}$ are given for each $\textbf{r}_{i}$ in the regions A-D.

To allow a direct visual comparison with the anatomical context, the values of
$\mathscr{m}$ together with the mean orientations are coded in a graphical
representation, i.e. as ellipses, and overplotted onto the widefield image in
Fig. 7. The orientation of the major axis in the ellipse denotes the mean
alignment direction, while the size of the minor-axis relative to the major
axis depicts the value of $\mathscr{m}$. Thereby, the minor-axis of the
ellipse was defined as the length of the major-axis (length of the major axis
is a constant arbitrary value chosen for graphical representation) multiplied
by the absolute value of $\mathscr{m}$.

Slope parameter $(\mathscr{m})$
---
A | B | C | D
$\textbf{r}_{1}$ : -0.99 |  $r_{1}$ : -0.69 |  $r_{10}$ : -0.48 |  $r_{1}$ : -0.25 |  $r_{1}$ : -0.37
$\textbf{r}_{2}$ : -1.02 |  $r_{2}$ : -0.72 |  $r_{11}$ : -0.42 |  $r_{2}$ : -0.18 |  $r_{2}$ : -0.24
$\textbf{r}_{3}$ : -1.00 |  $r_{3}$ : -0.67 |  $r_{12}$ : -0.41 |  $r_{3}$ : -0.20 |  $r_{3}$ : -0.25
$\textbf{r}_{4}$ : -0.89 |  $r_{4}$ : -0.61 |  $r_{13}$ : -0.36 |  $r_{4}$ : -0.02 |  $r_{4}$ : -0.41
$\textbf{r}_{5}$ : -0.96 |  $\textbf{r}_{5}$ : -0.89 |  $r_{14}$ : -0.34 |  $r_{5}$ : -0.27 |  $r_{5}$ : -0.52
$\textbf{r}_{6}$ : -0.95 |  $r_{6}$ : -0.63 |  $r_{15}$ : -0.22 |  $r_{6}$ : -0.21 |  $r_{6}$ : -0.52
|  $r_{7}$ : -0.73 |  $r_{16}$ : -0.19 |  $\textbf{r}_{7}$ = -0.98 |  $r_{7}$ : -0.46
|  $r_{8}$ : -0.68 |  $r_{17}$ : -0.25 |  |
|  $r_{9}$ : -0.60 |  $r_{18}$ : -0.13 |  |
|  |  $r_{19}$ : -0.08 |  |
Table 1: Slope parameter $(\mathscr{m})$, quantified from the curves in Fig.
5(a,c) and 6(a,c) of each measurement point: $\textbf{r}_{i}$ in Fig. 1. The
value of $\mathscr{m}$ varies from 0 (indicating a high degree of alignment)
to -1 (indicating a zero degree of alignment). Bold = gray matter, regular =
white matter Figure 7: Ellipse-encoded visualization of mean alignment
direction and degree of alignment for different measurement points
($\textbf{r}_{i}$) in regions (A-D). The ellipses are superimposed on the
white light widefield image of the tissue surface. The red circles represent
the position of the probing beam. The orientation of the ellipses encodes the
estimated mean alignment direction and the aspect ratio encodes the degree of
alignment. For high degree of alignment the ellipse approaches a line, while
for zero degree of alignment it becomes a circle (eg. region: A). GM: Gray
Matter, CC: Corpus Callosum, EC: External Capsule, IC: Internal Capsule and
PCG: Pre-Central Gyrus. Note that the length of the ellipse axis can vary from
one region to another due to the different scalings.

In all points $\textbf{r}_{i}$ located inside the gray matter, our results
indicate a very low to zero degree of alignment. This is visualized by the
circularity of the ellipses, which corresponds to $\mathscr{m}$ values
persistently found around $\mathscr{m}$ = -1, i.e. in-between -0.89 and -1.02
(see table 1, bold values). In comparison, for points located in white matter
the ellipses deviate substantially from the circular shape ($\mathscr{m}$
values range from -0.03 to -0.73). In the most extreme case, inside the corpus
callosum in Fig. 7 region C, the ellipses are flat close to a line,
representing low and fairly constant $\mathscr{m}$ values between -0.03 and
-0.27. Such strong degree of orientation can be expected since the corpus
callosum contains a rather uniform density of well aligned in-plane nerve
fibers running parallel to a common axis [46, 47].

The measurements within the white matter in region D provide a more
differentiated picture reflecting its anatomical perculiarities. The fine
local differences in $\mathscr{m}$ showcase the sensitivity of the
$\mathscr{m}$ values to small variations in tissue architecture. The mean
orientation indicated by the main axis of the ellipses runs parallel to a
virtual trajectory that reflects the direction of the nerve fibers running
from the gyrus towards the center of the brain [46]. Along this trajectory,
the $\mathscr{m}$ values indicate a continuous variation of the degree of
alignment. Starting from a medium degree of alignment near the bifurcation of
white matter at ${r}_{1}$, the degree of alignment increases to a maximum at
the narrowest part medial to this bifurcation (${r}_{2}$ and ${r}_{3}$), and
then decreases again towards the next bifurcation (${r}_{4}$ to ${r}_{7}$).
This behaviour can on one hand be explained by association, commissurial, and
projection fibers that intersect with a larger variety of angles leading to a
lower degree of alignment at bifurcations than at the narrow part between
sulci, but on the other hand by a higher prevalence of crossing U fibers
oriented at different planes in areas where the white matter is thicker.

A similar observation of gradually changing orientation and ellipticity is
made in region B. The degree of alignment is indicated to be strongest inside
the external capsule (${r}_{15}$ to ${r}_{19}$, $\mathscr{m}$ values ranging
between -0.25 and 0.08) with a mean orientation consistently pointing along
the axis of this structure. Both observations agree well with the expected
alignment of densely packed nerve fibers connecting the putamen and the
claustrum. In comparison, the degree of alignment is indicated to be
substantially lower around the sulcus towards the pre-central gyrus and the
mean orientation in the different points follows the curvature of this sulcus
(${r}_{1}$ to ${r}_{10}$, $\mathscr{m}$ values between -0.73 and -0.48). The
transition is again continuous with a medium degree of alignment indicated in
${r}_{11}$ to ${r}_{14}$ located at the upper end of the external capsule. The
low degree of alignment around the sulcus can be explained by a crossing of
nerves fibers from the external capsule with the fibers of the corona radiate
system exiting the internal capsule in the same area, and by fibers from the
arcuate fasciculus running perpendicular to the section plane [21].

The observed qualitative correlation of $\mathscr{m}$ along fiber trajectories
and their correspondence to anatomical structures in the brain indicate that
our results are indeed sensitive to small variations in tissue architecture. A
more quantitative assessment of the possible accuracy of this technique can be
obtained when calculating the standard deviation (std) of $\mathscr{m}$ within
groups of measurement points. For gray matter in region A, the std is 0.044,
and for white matter in region C (corpus callosum), it is 0.088. In region B
(external capsule), we distinguish four groups within which $\mathscr{m}$ is
fairly constant. The std are 0.046 (${r}_{1}$ to ${r}_{4}$), 0.098 (${r}_{6}$
to ${r}_{10}$), 0.040 (${r}_{11}$ to ${r}_{14}$), and 0.070 (${r}_{15}$ to
${r}_{20}$). Assuming that the degree of alignment was constant within each of
these groups, the std gives an upper bound of the achieved accuracy (whereas
the actual accuracy can be even better, if part of the observed variations is
explained by the tissue structure). Apart from two outliers, the std values
are consistently found around 0.05, indicating that the measured differences
between the different groups in region B are indeed significant (the mean
values are 0.673, 0.642, 0.382, and 0.176) and correspond to actual variations
of tissue architecture along the external capsule.

##  4 Conclusion

In this study, we used polarimetric imaging to investigate the structural
anisotropy of different regions in a coronal cross-section of a human brain.
Our results demonstrate the possibility to clearly distinguish the two
structurally distinct tissue types constituting the human brain, i.e., gray
and white matter, by analyzing the tissue’s backscattered polarimetric
response. Here, the widefield images in which the two tissue types can
visually be discerned serve as a reference. By defining a slope parameter
$\mathscr{m}$, which provides an intuitive understanding of the degree of
alignment of the micro-architecture in the tissue, we observed that there is a
strong correlation between the $\mathscr{m}$ values and the tissue structure.
Values close to -1 are consistently found in gray matter, indicating isotropic
behavior and rotational symmetry, which is expected due to the isotropic
distribution of cell bodies in gray matter. Values mostly in the range between
-0.5 and 0 are found in white matter, indicating a high degree of alignment,
which corresponds to the prevalence of nerve fiber bundles. The estimated mean
alignment direction found in white matter is in agreement with the nerve
fibers pathways in the brain [46, 48]. Further, the analysis of regions B and
D suggests that we can sensitively distinguish small nuances in the degree of
alignment of nerve fibers in the white matter. This allows us to visualize the
gradual transition of $\mathscr{m}$ from regions with high degree of alignment
where associaction, commissural, and projection fibers run parallely in one
direction, to regions of lower degree of alignment where the fibers are
intertwined, located in different planes and where U fibers are present. The
assumption that these qualitative observations relate to actual tissue
architecture is supported by the analysis of the std of $\mathscr{m}$ within
spatial groups. Assuming that the degree of alignment does not vary
significantly within these areas, the std serves as an upper bound of the
achievable accuracy of determining $\mathscr{m}$.

In conclusion, the results suggest that the proposed technique allows to
sensitively define the different degrees of alignment in healthy brain tissue
in-vivo without prior tissue preparation. On one hand, it could be used to
help accurate delineation of cancer tissue during resection. On the other
hand, given the promising sensitivity of distinguishing nuances in degree of
alignment inside white matter, it could be used to guide resections by
identifying vital nerve fiber trajectories by performing tractography of nerve
fiber pathways in the brain. In addition to applications in the brain, the
presented method has potential to identify pathologies in other tissue types
consisting of fibrous structures, such as the skin for diagnosing skin cancer
or for monitoring the healing process after skin injuries.

## Acknowledgment

The Authors would like to thank René Nyffenegger and Manes Hornung for their
valuable inputs and Ekkehard Hewer from the Institute of Pathology, University
Hospital Bern for providing the brain sample. We thank Lynn Roth and André
Stefanov for many stimulating discussions and proof-reading and Florentin
Spadin for helping with the figures.

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