text:
\section{Introduction}
\label{sec:introduction}

The human brain consists of a huge network of nerve fibers: Around 100 billion nerve cells are connected to 10,000 other nerve cells on average \cite{gilbert2000,herculano2009,kandel,squire2008,longstaff2011}. Understanding the structure and function of the brain remains a key challenge for neuroscience. To figure out how brain function emerges from its structural organization, it is necessary to study the neuronal connections, \ie, the three-dimensional nerve fiber architecture of the brain. Developing a detailed network model of the brain, the so-called \textit{connectome} \cite{behrens2012,shi2017}, reveals connected brain regions and helps to identify important nerve fiber connections, which is a prerequisite for brain surgery.
It also serves as a reference for fiber tractography algorithms, improving the interpretation of clinical data obtained from diffusion magnetic resonance imaging (MRI) \cite{mori2006, beaulieu2002, tuch2003}. Finally, the connectivity of the nerve fibers exposes pathological changes in the brain's tissue structure, allowing to study neuro-degenerative diseases like Alzheimer's or Parkinson's disease and to develop new treatments and tools for improved diagnostics.
To visualize and derive brain tissue properties and organization principles, light-microscopy techniques are widely used \cite{golgi1873,cajal1904,nieuwenhuys2012}.

In this paper, we study how the scattering of light can be used to improve the interpretation of light microscopy images from fibrous tissue samples like brain tissue. For this purpose, we have developed a simulation framework that models light scattering in transmission microscopy measurements and allows an improved interpretation of the measured data by delivering 3D information about the underlying fiber structure.

Technological progress and new advances in tissue preparation and labeling have enabled the development of techniques that reveal the 3D nerve fiber architecture in both living and post-mortem brains \cite{osten2013},
such as Optical Coherence Tomography \cite{men2016,magnain2015,benArous2011}, Micro-Optical Sectioning Tomography \cite{li2010}, Light-Sheet Microscopy \cite{susaki2014,costantini2015,mertz2010,stefaniuk2016,silvestri2014} or \textit{Two-Photon Fluorescence Microscopy (TPFM)} \cite{wang2013,zong2017,amato2016,kawakami2012, silvestri2014}.
While most of these techniques are limited to small sample sizes, the neuroimaging technique \textit{3D Polarized Light Imaging (3D-PLI)} \cite{MAxer2011_1,MAxer2011_2} allows to study the nerve fiber architecture of whole post-mortem brains with microscopic resolution: unstained histological brain sections are illuminated by polarized light and the birefringence caused by the highly anisotropic structure of the nerve fibers is measured, thus revealing their spatial orientations \cite{menzel2015}.

Such neuroimaging techniques require special instruments that are not available in each laboratory. Many laboratories are equipped with simple transmission microscopes which only extract 2D information of the investigated tissue structures, making it difficult to reconstruct complex nerve fiber architectures across several brain sections.
Here, we show that conventional bright-field transmission microscopy measurements can be used to obtain information about the 3D fiber structure of a sample, without need to change the experimental setup or to repeat measurements: the polarization-independent intensity of light that is transmitted through the sample (\textit{transmittance}) depends on the orientation of the fibers with respect to the light beam, \ie, the transmittance of a brain section provides information about the out-of-plane \textit{inclination} angle of the enclosed nerve fibers. These findings can also be transferred to other biological and non-biological samples with comparable fibrous structures, \eg, muscle fibers, collagen, or artificial fibers.

The correct reconstruction of nerve fiber crossings is a major challenge for many neuroimaging techniques and a prerequisite for the correct interpretation of clinical MRI data, allowing for better diagnostics and treatments of neuro-degenerative diseases.
In standard 3D-PLI measurements, brain regions with in-plane crossing fibers cannot be distinguished from regions with out-of-plane fibers or regions with low fiber densities because they all yield small birefringence signals. So far, only the strength and phase of the birefringence signal are used to derive the spatial fiber orientations. The transmittance, which is the average value of the signal, has not been used for this purpose. Here, we demonstrate that the transmittance cannot only be used to gain information about the out-of-plane inclination of the fibers, but also to classify these regions and to identify crossing fibers that cannot unambiguously be determined with standard polarization microscopy techniques.

The transmittance is a measure of how much the light is attenuated when it passes through the brain tissue, \ie, it depends on tissue absorption as well as scattering of light. As the absorption coefficient of brain matter is small (less than 0.1\,mm$^{-1}$ \cite{schwarzmaier1997,yaroslawsky2002}), the measured transmittance is expected to be mainly influenced by scattering. To study such complex light-tissue interactions at the microscopic level, we employed \textit{finite-difference time-domain (FDTD)} simulations to compute the propagation of the light wave through the brain tissue sample \cite{taflove,menzel2016,wilts2014,DeRaedt2012,wilts2012}.
FDTD simulations are a proven tool for studying for example light scattering in lithography applications \cite{taflove2013,azpiroz2008,erdmann2006} or nanostructures \cite{mcmahon2010,grimault2006,irannejad2013}. They have also been applied to investigate microscopy measurements of non-biological and biological tissue samples \cite{taflove2013,drezek2000,kosmas2004}, but not yet to brain tissue. One reason might be that simulations of tissue samples with dimensions of several micrometers are computationally very intense because the mesh size in the simulation needs to be much smaller than the wavelength. To still enable the investigation of larger samples like brain tissue, we used high-performance computing and a simplified simulation model for the optics of the imaging system and the inner structure of the nerve fibers.
The developed simulation framework can easily be adapted to microscopy techniques with different optics (wavelength, polarization of light, numerical aperture, etc.) and tissue samples with comparable fibrous structures.

The paper is divided in an experimental and a simulation part:
In \cref{sec:exp-studies}, we evaluate experimental data and develop techniques to obtain structural 3D information from transmittance images of samples with unknown substructure: we study measurement results obtained from brain sections of different species (rodent, monkey, human) and show that the transmittance decreases significantly (by more than 50\%) with increasing out-of-plane inclination angle of the nerve fibers, using both 3D-PLI and TPFM measurements to access the fiber inclination.
In \cref{sec:sim-studies}, we introduce the FDTD simulation framework and present the simulation results for artificial nerve fiber configurations with different inclination and crossing angles. The simulations show that the decrease in transmittance is mainly caused by isotropic light scattering and by the finite numerical aperture of the imaging system. The in-plane crossing angle of the fibers has no impact on the transmittance and can be determined from the respective scattering pattern.
In \cref{sec:exp-sim}, we combine the simulation results with experimental data and show that the transmittance can be used to distinguish between regions with in-plane crossing fibers, regions with out-of-plane fibers, and regions with low fiber density by combining the transmittance and the strength of the measured birefringence signal.

\section{Experimental studies}
\label{sec:exp-studies}

In this section, various experimental studies are presented that evaluate how the transmittance of brain sections depends on the out-of-plane inclination angle of the enclosed nerve fibers.
For our studies, we mostly used 3D-PLI measurements as they provide both the transmittance and the three-dimensional nerve fiber orientations independently from each other \cite{MAxer2011_1, MAxer2011_2}.
As both scattering and absorption contribute to the attenuation (transmittance) of light, differences in the transmittance might not only be caused by different fiber inclinations, but also by a different tissue composition or density.
To investigate the inclination dependence independently from tissue composition or preparation, we performed our studies on different species, subjects, and brain sections.

The studies were conducted on healthy brains from mice, rats, vervet monkeys, and humans. All brains were obtained directly after death in accordance with legal and ethical requirements. The brains were deeply frozen, cut into sections of 60\,\textmu m thickness, embedded in a solution of 20\% glycerin, and cover-slipped.
A detailed description of the brain preparation can be found in \cref{sec:brain-preparation}.
The brain sections were measured with 3D-PLI, using a polarimeter with a numerical aperture of 0.15 and an object-space resolution of about 1.33\,\um\,/\,px \cite{MAxer2011_1,MAxer2011_2}. The polarimeter consists of an LED light source, a rotating linear polarizer, a specimen stage containing the brain section, a circular polarization analyzer, and a camera which records the transmitted light intensity for different rotation angles $\{0^{\circ}, 10^{\circ}, \dots, 170^{\circ}\}$ of the polarizer. More information about the 3D-PLI measurement can be found in \cref{sec:3DPLI}. The signals provide information about the spatial orientations of the nerve fibers.
The amplitude of the signal (\textit{retardation} $\vert\sin\delta\vert$) is related to the birefringence of the brain section and served here as a measure of the out-of-plane fiber inclination angle $\alpha$, using $\delta \propto \cos^2\alpha$ \cite{menzel2015}.
The transmittance was computed from the same signal without additional measurements by averaging the measured light intensities over all rotation angles. (For an ideal system, conventional transmission microscopy with unpolarized light should yield the same result.) To only consider effects caused by the brain tissue, the resulting transmittance values were normalized for each image pixel by the average transmitted light intensity without sample,
yielding the \textit{normalized transmittance} $I_{\text{T,N}}$.

\subsection{Transmittance of flat and steep nerve fibers}
\label{sec:transmittance-flat-steep}

\begin{figure}[!t]
	\centering
	\includegraphics[width=\columnwidth]{Fig_Rat_Vervet_Atlas}
	\caption{Transmittance and retardation images of coronal and sagittal brain sections for a rat (\textbf{a}) and a vervet monkey (\textbf{b}). The coronal (sagittal) section planes are indicated by blue (red) lines in the respective other brain section for reference, selected anatomical structures are labeled (see legend). The upper two rows of each panel show the normalized transmittance images $I_{\text{T,N}}$, the third row shows the retardation images $\vert\sin\delta\vert$, both obtained from 3D-PLI measurements with 1.33\,\um\ pixel size. The images in the first row show the whole brain section, the images in the second and third row show an enlarged view. The selected regions in yellow (green) belong to steep (flat) nerve fibers, which appear dark (bright) in the transmittance and retardation images.}
	\label{fig:Rat_Vervet_Atlas}
\end{figure}

In order to study how the transmittance depends on the out-of-plane inclination angle of the nerve fibers, the substructure of the investigated brain section needs to be taken into account.
In large anatomical structures with densely packed nerve fibers, however, the inclination angles of the nerve fibers cannot be exactly determined by 3D-PLI or TPFM measurements. Instead, we compared the transmittance of \textit{flat} nerve fibers (with inclination angles $\alpha < 45^{\circ}$) to the transmittance of \textit{steep} nerve fibers ($\alpha > 45^{\circ}$) by investigating sections from brains that were cut along mutually orthogonal anatomical planes:
one brain was cut along the \textit{coronal} plane (dividing the brain into back and front), the other brain was cut along the \textit{sagittal} plane (dividing the brain into left and right).
As the sagittal plane is oriented perpendicular to the coronal plane, the transmittance of the same brain region can be evaluated for flat nerve fibers in one section plane and for steep nerve fibers in the other section plane.
Since different brain sections from different specimens might not be comparable due to differences in the tissue structure, we only compared the transmittance values within the same brain section.

\Cref{fig:Rat_Vervet_Atlas} shows the normalized transmittance images $I_{\text{T,N}}$ of coronal and sagittal sections from rat and vervet monkey brains.
The coronal (sagittal) section planes are indicated by blue (red) lines in the respective other brain section for reference.
Selected brain structures were identified according to rat \cite{zilles1985,paxinos2007,papp2014} and vervet \cite{woods2011,vervetatlas,zilles2015} brain atlases.
The transmittance values were evaluated in brain regions that have a relatively homogeneous tissue composition and that include predominantly flat nerve fibers (areas surrounded in green) or steep nerve fibers (areas surrounded in yellow).

The approximate orientation of the nerve fibers is known from the anatomy of the rat and the vervet brain as described in the atlases, and was confirmed by the retardation images $\vert\sin\delta\vert$ shown below the transmittance images in \cref{fig:Rat_Vervet_Atlas}: regions with flat nerve fibers show larger retardation values than regions with steep nerve fibers.
The mean transmittance values and the standard deviation for the evaluated green and yellow areas can be found in \cref{tab:Rat_Vervet_Transmittance}.
\begin{table}[!htb]
	\caption{Mean transmittance values ($\overline{I_{\text{T,N}}}$) and standard deviation for the selected green and yellow areas in \cref{fig:Rat_Vervet_Atlas}. Areas belonging to the same structure were evaluated together (cg $\equiv$ cg1 $\cup$ cg2).
		}
	\label{tab:Rat_Vervet_Transmittance}
	\begin{center}
		\begin{tabular}{c|cc|cc} 	\hline\hline
			\multicolumn{1}{c}{} 	& \multicolumn{2}{c}{Rat}					&  	\multicolumn{2}{c}{Vervet}		\\
				&	Coronal			&  Sagittal			& Coronal				& Sagittal							\\ \hline
			ac	&	--				& --				& -- 	& \fcolorbox{yellow}{white}{$0.11 \pm 0.04$} 		\\
			cc	&	\fcolorbox{green}{white}{$0.33 \pm 0.16$}	& \fcolorbox{yellow}{white}{$0.09 \pm 0.04$}
				& 	\fcolorbox{green}{white}{$0.24 \pm 0.09$} 	& \fcolorbox{yellow}{white}{$0.11 \pm 0.05$}		\\
			cg	&	\fcolorbox{yellow}{white}{0.15 $\pm$ 0.06}	& \fcolorbox{green}{white}{0.18 $\pm$ 0.09}
				&  	\fcolorbox{yellow}{white}{0.08 $\pm$ 0.02} 	& \fcolorbox{green}{white}{0.24 $\pm$ 0.09} 		\\
			df	&	\fcolorbox{yellow}{white}{$0.10 \pm 0.03$}	& -- & -- & --										\\
			f	&	--	& -- & \fcolorbox{yellow}{white}{$0.13 \pm 0.06$}& \fcolorbox{green}{white}{$0.26 \pm 0.10$}	\\
			fi	&	\fcolorbox{green}{white}{$0.25 \pm 0.10$}	& \fcolorbox{yellow}{white}{$0.15 \pm 0.07$} 	& -- & --	\\
			sm	&	\fcolorbox{yellow}{white}{$0.08 \pm 0.03$}	& -- & -- & --	\\[5pt]\hline\hline
		\end{tabular}
	\end{center}
\end{table}

In regions with flat nerve fibers, the mean transmittance values are larger ($\overline{I_{\text{T,N}}} \in [0.18, 0.33]$) than in regions with steep nerve fibers ($\overline{I_{\text{T,N}}} \in [0.08, 0.15]$). A region with flat (steep) nerve fibers which shows large (small) transmittance values in one section plane (coronal or sagittal), shows the opposite behavior in the corresponding orthogonal section plane. The difference is especially large when comparing the transmittance values of the \textit{corpus callosum} (a massive fiber tract connecting the two hemispheres of the brain) and the \textit{cingulum} (a C-shaped fiber structure running mostly perpendicular to the corpus callosum). In the coronal brain sections, the fibers of the cingulum (cg) run mostly perpendicular to the section plane and have about 55--67\% lower transmittance values than the fibers of the corpus callosum (cc) which lie mostly within the section plane. In the sagittal brain sections, the situation is exactly the opposite: the transmittance values of the corpus callosum are about 50--54\% less than the transmittance values of the cingulum. Fibers in the rat and vervet monkey brains show a similar pattern.

As expected, images obtained from conventional bright-field transmission microscopy with unpolarized light show similar effects, not only in vervet but also in human brain sections (see \cref{fig:Human_PLI-vs-Zeiss} and Fig.\ S\ref{fig:Vervet_PLI-vs-Zeiss} in the Supplemental Material): regions with steep (out-of-plane) nerve fibers appear darker than regions with flat (in-plane) nerve fibers.

\begin{figure}[!t]
	\centering
	\includegraphics[width=\columnwidth]{Fig_Human_PLI-vs-Zeiss_}
	\caption{Bright-field transmission microscopy (see \cref{sec:bright-field}) vs.\ 3D-PLI measurement of a human brain section (right occipital lobe). (\textbf{a}) Photograph of the brain block surface before sectioning (blockface image). The enlarged region shows the \textit{sagittal stratum}, a white matter structure that runs mostly perpendicular to the section plane (GM = gray matter). (\textbf{b}) Bright-field transmission microscopy image of the same region with 0.91\,\um\ pixel size. (\textbf{c}) Normalized transmittance image of the same region obtained from a 3D-PLI measurement with 1.33\,\um\ pixel size. (\textbf{d}) Corresponding retardation image. Regions with steep out-of-plane fibers (\textit{sagittal stratum}) show lower transmittance (and retardation) values than the neighboring regions with non-steep fibers; the transmitted light intensity images obtained from bright-field transmission microscopy (b) and 3D-PLI (c) look similar.}
	\label{fig:Human_PLI-vs-Zeiss}
\end{figure}

\subsection{3D-reconstruction of transmittance images}
\label{sec:3D-transmittance}

So far, single brain sections from different specimens were compared to each other. To study the transmittance across several consecutive brain sections, the transmittance images of 234 coronal sections from the right hemisphere of a vervet monkey brain were registered onto each other using in-house developed software tools (see \cref{sec:3DPLI}).
\Cref{fig:3D-Transmittance} shows the 3D-reconstructed transmittance images along three orthogonal anatomical planes: coronal (a), sagittal (b), and horizontal (c), as well as a detail of the 3D-volume (d). The white arrows point to the \textit{sagittal stratum} -- a white matter structure with nerve fibers that are oriented mostly perpendicular to the image plane (along the z-direction), as can be seen in the sagittal and horizontal planes. The structure appears much darker in the transmittance images than the surrounding regions.
Thus, the observation that steep nerve fibers show lower transmittance values than flat nerve fibers is consistent across several consecutive brain sections.

\begin{figure}[!t]
	\centering
	\includegraphics[width=0.7\columnwidth]{Fig_3D-Transmittance_}
	\caption{3D-reconstructed normalized transmittance images ($I_{\text{T,N}}$) of the right hemisphere of a vervet monkey brain (234 consecutive sections from the occipital lobe) obtained from 3D-PLI measurements with 1.33\,\um\ pixel size. The brain was cut along the coronal plane (xy-plane), the resulting brain sections were registered onto each other in the z-direction. (\textbf{a})-(\textbf{c}) Cross-sections of the 3D-volume shown along the coronal (xy), sagittal (xz), and horizontal (yz) plane. The colored lines indicate the position of the displayed xy-, xz-, and yz-planes. (\textbf{d}) Detail of the 3D-volume. The white arrows point to the \textit{sagittal stratum} -- a white matter structure that runs mostly perpendicular to the image plane (along the z-direction) and which appears much darker in the transmittance images than the surrounding tissue.}
	\label{fig:3D-Transmittance}
\end{figure}

\subsection{Transmittance contrast of nerve fiber bundles in mutually orthogonal planes}
\label{sec:transmittance-contrast}

\begin{figure*}[!t]
	\centering
	\includegraphics[width=1.5\columnwidth]{Fig_Rat_CPu}
	\caption{Transmittance contrast of nerve fiber bundles in mutually orthogonal anatomical planes. (\textbf{a}) Normalized transmittance images ($I_{\text{T,N}}$) of a coronal, sagittal, and horizontal rat brain section obtained from 3D-PLI measurements with 1.33\,\um\ pixel size. The colored lines indicate the approximate position of the section planes. The enlarged views show the region of the caudate putamen and the maximum and minimum angles under which the nerve fiber bundles are oriented with respect to the section planes. (\textbf{b}) Corresponding retardation images ($\vert\sin\delta\vert$) of the enlarged views. The image contrast was used to select regions with fibers and with surrounding tissue in the caudate putamen (yellow lines). (\textbf{c}) Histograms of the transmittance values ($I_{\text{T,N}}$) for the selected regions with nerve fibers (pink) and with surrounding tissue (cyan) in the caudate putamen. For the coronal brain section, the retardation image cannot be used to separate the fibers from the surrounding tissue because the fibers are oriented almost perpendicular to the image plane which leads to a small retardation signal and a small image contrast. Therefore, the histogram was computed over the whole selected region and the peak with lower (larger) transmittance was assumed to belong to fibers (surrounding tissue). The contrast values were computed from the respective peak values (numbers in pink and cyan) via: $\mathcal{C}$ = (max - min)/(max + min). The contrast for steep nerve fibers (coronal brain section) is much larger than for flat nerve fibers (sagittal and horizontal brain section).}
	\label{fig:Rat_CPu}
\end{figure*}

In the previous studies, we considered bulk tissue with densely packed nerve fibers where the fiber inclinations cannot be exactly determined. In regions with distinct fiber bundles, however, the inclination angles can be estimated by manually evaluating the course of the fiber bundles in different section planes. For this purpose, we selected a structure in the rat brain that contains several distinct nerve fiber bundles with different, well-defined inclination angles -- the so-called \textit{caudate putamen}. To estimate the inclination angles of the nerve fibers, we evaluated the course of the bundles in mutually orthogonal section planes (coronal, sagittal, horizontal), see \cref{fig:Rat_CPu}(a).
As the brain sections were obtained from different brains and might differ in tissue composition, the transmittance images cannot be directly compared to each other. To still enable a comparison between the transmittance of flat and steep nerve fibers, the transmittance values in regions with fibers were compared to the transmittance values in regions with surrounding tissue for each brain section, assuming that the transmittance of the surrounding tissue does not depend much on the choice of the section plane.

To separate the fiber bundles from the surrounding tissue, we used the image contrast of the retardation images (see yellow lines in \cref{fig:Rat_CPu}(b)). \Cref{fig:Rat_CPu}(c) shows the
corresponding histograms of the transmittance evaluated in regions with nerve fibers (pink) and in regions with surrounding tissue (cyan). As the coronal brain section contains mostly steep nerve fibers which yield low retardation values, the image contrast in the retardation image is not large enough to separate the fibers from the surrounding tissue. Therefore, we computed the histogram for the whole caudate putamen (area surrounded by yellow line) and assumed that the peak with lower (larger) transmittance belongs to nerve fibers (surrounding tissue).

From the minimum and maximum peak transmittance values of the histograms (pink and cyan numbers in \cref{fig:Rat_CPu}(c)), we computed the transmittance contrast $\mathcal{C} \equiv (I_{\text{T,max}} - I_{\text{T,min}})/(I_{\text{T,max}} + I_{\text{T,min}})$ between fiber bundles and surrounding tissue. For flat fiber bundles in the sagittal and horizontal brain sections, this contrast is much lower ($5^{\circ} \leq \alpha \leq 60^{\circ}$: $\mathcal{C} \approx 14$--$20\%$) than for steep fiber bundles in the coronal brain section ($45^{\circ} \leq \alpha \leq 85^{\circ}$: $\mathcal{C} \approx 62\%$). Assuming that the transmittance of the surrounding tissue is mostly independent of the fiber orientation, this demonstrates again that the transmittance values for steep nerve fibers are significantly lower than for flat nerve fibers.

\subsection{Transmittance vs. inclination of nerve fiber bundles in TPFM images}
\label{sec:transmittance-inclination-TPFM}

The previous studies were only qualitative and the observed differences in the transmittance might also be caused by a different tissue composition, \eg, a different density of nerve fibers. To quantitatively study how the transmittance of a brain section depends on the inclination angles of the enclosed nerve fibers, the exact underlying fiber structure of the investigated brain section needs to be known. Therefore, we measured the caudate putamen of a coronal mouse brain section both with 3D-PLI and with TPFM to identify the inclination angles of the enclosed fiber bundles (see inset in \cref{fig:Sim_Transmittance_vs_Inclination}(d) and Fig. S\ref{fig:PLI_vs_TPFM} in the Supplemental Material).

The TPFM measurements were performed with a custom-made two-photon fluorescence microscope which achieves a resolution of $0.244 \times 0.244 \times 1\,\um^3$ and allows to perform an in-depth-scan of the brain section (see \cref{sec:TPFM} for more details). To obtain the inclination angles of the fiber bundles, the cross-sections of the bundles were determined in the first and the last slice of the TPFM image stack (cf.\ Fig.\ S\ref{fig:PLI_vs_TPFM}(d)). For each fiber bundle, the inclination angle was computed from the mid points of the corresponding cross-sections and from the thickness of the brain section (cf.\ Fig.\ S\ref{fig:PLI_vs_TPFM}(c)).
The fiber inclination and transmittance values were evaluated for 40 fiber bundles in the caudate putamen (see colored shapes in Fig.\ S\ref{fig:PLI_vs_TPFM}(b),(d)).

The scatter plot in \cref{fig:Sim_Transmittance_vs_Inclination}(d) shows the averaged transmittance values plotted against the determined fiber inclination angles.
Although the values are broadly distributed, the scatter plot shows a clear tendency towards a decrease in transmittance with increasing fiber inclination angle.
The values in orange belong to regions with lower fiber densities which might lead to overestimated transmittance values. However, the decrease in transmittance is also observed in regions with maximum fiber density (values in blue): while the mean transmittance values for flat nerve fibers ($\alpha < 50^{\circ}$) reach larger values ($ 0.1 < \overline{I_{\text{T,N}}} < 0.2$), the mean transmittance values for steep nerve fibers ($\alpha > 60^{\circ}$) are small ($\overline{I_{\text{T,N}}} < 0.05$).\\

All our experimental studies show that the transmittance of brain tissue decreases significantly (by more than 50\%) with increasing out-of-plane inclination angle of the enclosed nerve fibers.

\section{Simulation studies}
\label{sec:sim-studies}

Although the experimental studies clearly show that the transmittance depends on the inclination angle of the nerve fibers, they do not provide enough information to describe this effect in detail. Based on the experimental results alone, it is not possible to make any predictions or draw conclusions for the interpretation of measured data. To model and better understand the observed transmittance effects, we performed numerical simulations on artificial nerve fiber configurations. This has the advantage that the exact underlying fiber structure, and thus the inclination angles of the nerve fibers, are known -- also in bulk tissue with densely packed fibers.

As mentioned in \cref{sec:introduction}, the absorption coefficient of brain tissue is small so that the transmittance is expected to be mainly influenced by scattering. To study such complex light-matter interactions in microscopic detail, finite-difference time-domain (FDTD) algorithms are well suited. They discretize time and space, model the propagation of the light wave by approximating the spatial and temporal derivatives in Maxwell's curl equations by second-order central differences, and numerically compute the electromagnetic field components in space and time \cite{taflove,menzel2016,wilts2014,DeRaedt2012,wilts2012}.
As the mesh size of the spatial discretization needs to be much smaller than the wavelength (at most 25\,nm), simulations of tissue samples with dimensions of several micrometers are computationally very intense. We have developed a simulation framework that allows for the first time to use FDTD simulations to study larger samples of fibrous tissue. For this purpose, we used a simplified simulation model for the brain tissue samples and the optics of the imaging system.
We simulated the 3D-PLI measurement for various fiber configurations and evaluated the resulting transmittance values.

The artificial fiber configurations consist of about 700 fibers with uniformly distributed diameters between $1.0\,\um$ and $1.6\,\um$ and different fiber orientations. All fibers were generated in a volume of $30 \times 30 \times 30\,\um^3$ without intersections. The generation of the fiber configurations is described in \cref{sec:generation-fiber-config} in more detail.
Each fiber was represented by a simplified nerve fiber model, consisting of an inner axon with a constant radius and a surrounding myelin sheath with two layers, defined by different refractive indices (see \cref{sec:model-nerve-fibers} for motivation).

For the simulations of the 3D-PLI measurement, we used a conditionally stable FDTD algorithm to compute the propagation of the light wave through the tissue sample (artificial fiber configuration), described in more detail in \cref{sec:FDTD}. The resulting electric field components were processed with analytical methods taking all optical components of the polarimeter into account, including the objective lens (with numerical aperture NA $= 0.15$) and the camera detector (see \cref{sec:computation-light-intensities}).

The simulation studies were all performed for normally incident light with 550\,nm wavelength and for the simulation parameters listed in \cref{sec:sim-parameters}.
One simulation run (volume of $30 \times 30 \times 30\,\um^3$, mesh size of 25\,nm) took about 8000 core hours on the supercomputer JUQUEEN (using an MPI grid of $16 \times 16 \times 16$), allowing to perform many simulation runs with different parameters.
The accuracy of the simulation results is discussed in \cref{sec:error-estimation}.

\subsection{Simulated transmittance of inclined fibers}
\label{sec:simulated-transmittance}

To better understand the inclination dependence of the transmittance that we observed in our experimental studies, we generated an artificial \textit{bundle of densely grown fibers} (see \cref{fig:Sim_Transmittance_vs_Inclination}(a) and \cref{sec:densely-grown}) for different inclination angles $\alpha = \{0^{\circ}, 10^{\circ}, \dots, 90^{\circ}\}$, and computed the transmittance from a simulated 3D-PLI measurement.

\begin{figure*}[!t]
	\centering
	\includegraphics[width=1.5\columnwidth]{Fig_Sim_Transmittance_vs_Inclination}
	\caption{Transmittance of inclined fiber bundles. (\textbf{a}) 3D view and cross-sections through mid-planes for an artificial bundle of densely grown fibers shown exemplary for an inclination angle $\alpha=45^{\circ}$. (\textbf{b}) Light-scattering patterns obtained from 3D-PLI simulations for the bundle of densely grown fibers with $\alpha = 0^{\circ}$ and $70^{\circ}$. To compute the mean normalized transmittance values $\overline{I_{\text{T,N}}}$ for the numerical aperture of the imaging system (NA = 0.15), only wave vector angles $\theta_k \leq 8.6^{\circ}$ were considered (see red circles). The white circles represent steps of $\Delta\theta_k = 10^{\circ}$. (\textbf{c}) Simulated transmittance curves (mean transmittance $\overline{I_{\text{T,N}}}$ vs. inclination $\alpha$) for the bundle of densely grown fibers (i) and for a bundle with broad fiber orientation distribution (ii) for NA = 1 (orange curves) and NA = 0.15 (blue curves). The transmittance curves were normalized by the mean transmittance values of the horizontal bundles, respectively. The simulations were performed with the parameters specified in \cref{sec:sim-parameters}, using normally incident light with 550\,nm wavelength. (\textbf{d}) Mean normalized transmittance values $\overline{I_{\text{T,N}}}$ plotted against the nerve fiber inclination angles $\alpha$ determined respectively from 3D-PLI and TPFM measurements of nerve fiber bundles in a mouse brain section (see Fig.\ S\ref{fig:PLI_vs_TPFM} in the Supplemental Material). The values in blue belong to regions with similar (maximum) fiber density, the values in orange belong to regions with variable fiber density in which the transmittance might be overestimated. The error bars indicate the standard error of the mean for the evaluated transmittance values. Both experimental and simulated data show that the transmittance decreases with increasing fiber inclination.}
	\label{fig:Sim_Transmittance_vs_Inclination}
\end{figure*}

\Cref{fig:Sim_Transmittance_vs_Inclination}(b) shows the resulting scattering patterns (\ie, the intensity per wave vector angle $\theta_k$) of light transmitted through the sample for inclination angles $\alpha = 0^{\circ}$ and $70^{\circ}$. The white circles represent steps of $\Delta\theta_k = 10^{\circ}$, from $0^{\circ}$ (center) to $90^{\circ}$ (outer circle). The transmittance images and scattering patterns for all inclination angles can be found in Fig.\ S\ref{fig:Sim_TransmittanceImages} in the Supplemental Material.

For flat fibers ($\alpha < 45^{\circ}$), the light is mostly scattered under angles perpendicular to the principal axis of the fiber bundle (\ie, along the y-axis). For intermediate inclination angles, the light is scattered more and more in the direction of the fibers (\ie, in the positive x-direction). For an inclination angle of $70^{\circ}$, the light is broadly scattered in almost all directions (see \cref{fig:Sim_Transmittance_vs_Inclination}(b)).

Due to the numerical aperture of the employed imaging system (NA $\approx$ 0.15), light scattered under angles larger than $\arcsin(\text{NA}) \approx 8.6^{\circ}$ does not contribute to the measured transmittance images.
To study the effect of the finite numerical aperture on the measured transmittance values, we simulated the imaging system without aperture (NA = 1) considering light scattered under all angles, and with aperture (NA = 0.15) considering only light scattered under angles $< 8.6^{\circ}$ (indicated by the red circles in \cref{fig:Sim_Transmittance_vs_Inclination}(b)).

\Cref{fig:Sim_Transmittance_vs_Inclination}(c) shows the resulting transmittance curves (mean values of the simulated transmittance images plotted against the inclination angles of the fiber bundle) for NA = 1 (orange curves) and NA = 0.15 (blue curves). The solid curves were obtained from the bundle of densely grown fibers (i) which has similar fiber orientations (the mode angle difference between the local fiber orientation vectors and the predominant orientation of the fiber bundle is less than $10^{\circ}$). The dashed curves were obtained for a \textit{bundle with broad fiber orientation distribution} (ii) which contains many different fiber orientations (the mode angle difference is about $25^{\circ}$, see \cref{sec:inhom-fiberbundle}). To enable a better comparison between horizontal fiber bundles ($\alpha = 0^{\circ}$) and vertical fiber bundles ($\alpha = 90^{\circ}$), all curves were divided by the mean transmittance value of the horizontal bundle, respectively. Figure S\ref{fig:Sim_TransmittanceCurves}(a),(c) in the Supplemental Material shows the (normalized) transmittance curves in separate figures.

For NA = 1, the transmittance for steep fibers is similar to or even slightly larger than the transmittance for flat fibers.
For NA = 0.15, the transmittance decreases significantly between $\alpha = 30^{\circ}$ and $\alpha = 70^{\circ}$.
This implies that the observed decrease in transmittance is caused by the finite numerical aperture of the imaging system: for steep fibers, the light is scattered almost uniformly in all possible directions (cf.\ \cref{fig:Sim_Transmittance_vs_Inclination}(b) for $\alpha = 70^{\circ}$) so that the detected transmitted light intensity becomes minimal. In simulation studies with polarized light, we could show that the decrease in transmittance is independent of the direction of polarization (see \cref{fig:SimParameters_TransmittanceCurves}(a) in \cref{sec:error-estimation}) which suggests that the decrease is caused by isotropic (not by anisotropic) scattering of light.

While the transmittance for the bundle of densely grown fibers becomes minimal at $\alpha = 70^{\circ}$ for NA = 0.15 (the transmittance is 90\% less than the transmittance for the horizontal bundle) and the transmittance for vertical fibers ($\alpha = 90^{\circ}$) is only about 25\% less than for horizontal fibers ($\alpha = 0^{\circ}$), the transmittance for the bundle with broad fiber orientation distribution decreases monotonically with increasing fiber inclination angle and becomes minimal for vertical fibers (the transmittance for vertical fibers is more than 80\% less than for horizontal fibers).
Due to the broad fiber orientation distribution, the vertical bundle contains many fibers with inclinations between $60^{\circ}$ and $70^{\circ}$, which explains why the minimum transmittance is shifted to larger inclination angles.

Especially for the bundle with broad fiber orientation distribution, the simulated transmittance curves (\cref{fig:Sim_Transmittance_vs_Inclination}(c)) show a similar behavior as the measured transmittance values in the scatter plot (\cref{fig:Sim_Transmittance_vs_Inclination}(d)).\\

As mentioned in the beginning, the brain sections used for the 3D-PLI measurements are embedded in glycerin solution.
With increasing time after this tissue embedding, we observed that the brain sections become more and more transparent, \ie, the transmittance increases (see \cref{fig:Transmittance_vs_Time}).
To enable optimal transmittance contrasts, the brain sections were therefore measured directly after the embedding and the simulations were performed assuming that the refractive indices of the nerve fibers correspond to given literature values (see \cref{sec:model-nerve-fibers}).
With increasing time after the tissue embedding, the glycerin solution presumably soaks into the myelin sheaths which surround the axons. As the glycerin solution has a lower refractive index than the myelin lipids, the effective refractive index of the myelin sheaths is therefore expected to decrease. Figure S\ref{fig:Sim_TransmittanceCurves}(b) in the Supplemental Material shows the resulting transmittance curves for the bundle of densely grown fibers with a reduced myelin refractive index: the mean transmittance for steep fibers ($\alpha=70$--$80^{\circ}$) is only about 30\% less than the mean transmittance for horizontal fibers, and the absolute transmittance values become larger. This corresponds to the experimental observation that the transmittance increases with increasing time after the tissue embedding.

\begin{figure}[!t]
	\centering
	\includegraphics[width=0.6\columnwidth]{Fig_Transmittance_vs_Time_}
	\caption{Normalized transmittance images $I_{\text{T,N}}$ of the sagittal rat brain section in \cref{fig:Rat_Vervet_Atlas}(a) obtained from a 3D-PLI measurement one day after tissue embedding and 16 months later. With increasing time after the tissue embedding, the brain section becomes more transparent.}
	\label{fig:Transmittance_vs_Time}
\end{figure}

\subsection{Simulated transmittance of crossing fibers}
\label{sec:sim-transmittance-crossing}

Our previous simulation studies have shown that the transmittance strongly depends on the out-of-plane fiber inclination angle. Hence, the transmittance could be used to distinguish out-of-plane fibers from in-plane crossing fibers, which both yield small birefringence signals and can to date not be distinguished in standard 3D-PLI measurements.
To study this in more detail, we simulated the transmittance of horizontal (in-plane) crossing fibers for different crossing angles and compared the results to the transmittance of steep (out-of-plane) fibers.

The horizontal crossing fibers were generated as separate and interwoven fiber bundles (see \cref{sec:inhom-fiberbundle} and \cref{fig:CrossingFibers}(a)-(b)) with different crossing angles $\chi = \{0^{\circ}, 15^{\circ}, \dots, 90^{\circ} \}$.
\Cref{fig:Sim_CrossingFibers}(a) shows the resulting scattering patterns and normalized mean transmittance values $\overline{I_{\text{T,N}}}$ for NA = 0.15 and $\chi = \{90^{\circ}, 60^{\circ}, 30^{\circ} \}$.

\begin{figure*}[!htb]
	\centering
	\includegraphics[width=1.5\columnwidth]{Fig_Sim_CrossingFibers}
	\caption{Simulated transmittance of crossing fibers. (\textbf{a})-(\textbf{c}) 3D views and light-scattering patterns for (a) horizontal crossing fibers (separate bundles in the upper row, interwoven bundles in the lower row) with crossing angle $\chi$, (b) three mutually orthogonal, interwoven fiber bundles, and (c) a vertical fiber bundle with broad fiber orientation distribution (cf.\ \cref{fig:Sim_Transmittance_vs_Inclination}(c)(ii)). The mean normalized transmittance values $\overline{I_{\text{T,N}}}$ were computed from a simulated 3D-PLI measurement (with numerical aperture NA = 0.15). The simulations were performed with the parameters specified in \cref{sec:sim-parameters}, using normally incident light with 550\,nm wavelength. (\textbf{d}) Mean transmittance values for different crossing angles $\chi$ shown for in-plane crossing (solid curves) and out-of-plane fiber configurations (densely dotted curves). For better comparison, the values were divided by the mean transmittance value of the corresponding horizontal fiber bundle for $\chi=0^{\circ}$. Apart from the fiber configurations shown in this figure, the mean transmittance values are also displayed for the bundle of densely grown fibers (see \cref{fig:Sim_Transmittance_vs_Inclination}(c)(i)) for $\alpha = 70^{\circ}$ and $90^{\circ}$. While the scattering patterns show the crossing angles of in-plane crossing fibers (see (a)), the mean transmittance is mostly independent of the crossing angle and larger than the mean transmittance of out-of-plane fibers (see (d)).}
	\label{fig:Sim_CrossingFibers}
\end{figure*}

The scattering patterns of separate and interwoven crossing fiber bundles look similar for all crossing angles. The underlying fiber configuration, \ie, the crossing angle of the fiber bundles, is clearly visible in all scattering patterns.
The mean transmittance values for the interwoven fiber bundles are up to 13\% larger than those for the separate fiber bundles and in both cases mostly independent of the crossing angle.

\Cref{fig:Sim_CrossingFibers}(b) shows the scattering pattern for three mutually orthogonal, interwoven fiber bundles. The fiber configuration is similar to the horizontal $90^{\circ}$-crossing, interwoven fiber bundles, but one third of the fibers is oriented in the z-direction (see \cref{sec:inhom-fiberbundle} and \cref{fig:CrossingFibers}(c)).
This configuration leads to lower transmittance values than the horizontal crossing fibers.

\Cref{fig:Sim_CrossingFibers}(c) shows the scattering pattern for a vertical fiber bundle (bundle with broad fiber orientation distribution and $\alpha = 90^{\circ}$, cf.\ \cref{fig:Sim_Transmittance_vs_Inclination}(c)(ii)).
The scattering pattern looks clearly different from the scattering pattern of the horizontal crossing fibers and the mean transmittance is much lower.

\Cref{fig:Sim_CrossingFibers}(d) shows the mean transmittance values of the different fiber bundles for NA = 0.15 plotted against the crossing angle $\chi$ (in the case of horizontal crossing fibers). For better comparison, the values were divided by the mean transmittance value of the corresponding horizontal fiber bundle (for $\chi=0^{\circ}$), respectively.
The solid curves belong to the horizontal crossing fibers (separate and interwoven bundles), the densely dotted lines below belong to fiber constellations that contain vertical or steep fibers: the bundle of densely grown fibers for $\alpha = 90^{\circ}$ and $70^{\circ}$, the mutually orthogonal fiber bundles, and the bundle with broad fiber orientation distribution for $\alpha = 90^{\circ}$.\\

The transmittance curves of horizontal crossing fibers are similar for separate and interwoven fiber bundles. While the mean transmittance of the separate crossing fibers corresponds more or less to the mean transmittance of the horizontal fiber bundle for $\chi = 0^{\circ}$, the transmittance values of the interwoven crossing fibers slightly increase with increasing crossing angle (by max.\ 11\%).

For all simulated fiber bundles that contain vertical or steep fibers, the mean transmittance values (densely dotted lines) are more than 26\% less than for the horizontal crossing fibers (solid lines).
For interwoven crossing fibers, the transmittance value is reduced by more than one half when the horizontal crossing fibers are combined with a vertical fiber bundle (orthogonal bundles).
For the vertical bundle with broad fiber orientation distribution and the steep bundle of densely grown fibers (with $\alpha = 70^{\circ}$), the difference between the transmittance values is especially large: the transmittance is about 80--90\% less than for the horizontal crossing fibers.\\

Our simulations of crossing fiber bundles have shown that the transmittance for horizontal fibers is mostly independent of the crossing angle between the bundles and much larger than the transmittance for vertical fibers. This suggests that the transmittance values can be used to distinguish between horizontal crossing and vertical fibers in 3D-PLI measurements, and to detect vertical fibers within fiber crossings.

\section{Combination of experimental and simulation studies}
\label{sec:exp-sim}

In this section, we combine the results from the experimental studies and the simulation studies to develop a classification for brain regions with low birefringence signals that cannot be distinguished by 3D-PLI measurement. The simulations in \cref{sec:sim-transmittance-crossing} have shown that the transmittance does not depend on the crossing angle between in-plane nerve fibers. First, we verify this prediction by investigating the optic chiasm of a hooded seal \cite{dohmen2015} -- a region that contains fibers with crossing angles of around $90^{\circ}$ in the image plane (see \cref{fig:OpticChiasm}).

\begin{figure*}[!t]
	\centering
	\includegraphics[width=1.5\columnwidth]{Fig_OpticChiasm}
	\caption{Crossing nerve fibers in the optic chiasm of a hooded seal: (\textbf{a}) brain tissue before sectioning, (\textbf{b}) unnormalized transmittance and retardation images of the middle brain section obtained from 3D-PLI measurements with 1.33\,\um\ pixel size, (\textbf{c}) schematic drawing of the optic chiasm consisting of optic tracts (o.t.) and optic nerves (o.n.), (\textbf{d}) normalized histograms of the transmittance image ($I_{\text{T}}$) and retardation image ($\vert\sin\delta\vert$) for a region with mostly parallel fibers (blue) and a region with nearly $90^{\circ}$-crossing fibers (orange). Unlike the retardation, the transmittance does not depend on the crossing angles of the nerve fibers, only on the tissue density. More information about the sample can be found in \textsc{Dohmen} \ea\ \cite{dohmen2015} (Figs.\ (a) and (c) were adapted from Figs.\ 1B and 5B0 in \cite{dohmen2015} Copyright (2015), with permission from Elsevier).}
	\label{fig:OpticChiasm}
\end{figure*}

While the retardation values in the region with crossing fibers (region B in orange) are broadly distributed (the birefringence signals of crossing fibers cancel out), the transmittance values in this region show a similar distribution as in a region with mostly parallel fibers (region A in blue), see histograms in \cref{fig:OpticChiasm}(d).

The peak transmittance value of region B is slightly lower than in region A because the number of fibers in the crossing region (two crossing bundles) is larger than in the region with parallel fibers (one bundle). Thus, the transmittance depends on the tissue density, but not on the crossing angles between the nerve fibers -- as predicted by the simulations in \cref{sec:sim-transmittance-crossing}.

To demonstrate that the transmittance can be used to classify regions with small birefringence signals (\ie, small retardation values obtained from 3D-PLI measurements) into regions with in-plane crossing fibers, regions with steep fibers, and regions with low fiber density, the predictions obtained from the simulation studies in \cref{sec:sim-studies} were applied to experimental data (see \cref{fig:Transmittance_vs_Retardation}).

As the transmittance depends on absorption, the region with maximum absorption was determined as a reference:
The retardance $\delta$ of brain tissue increases with decreasing fiber inclination angle $\alpha$ and with increasing thickness $d$ of birefringent tissue components ($\delta \propto d\,\dn \, \cos^2\alpha$, where $\dn$ is the birefringence of the tissue \cite{MAxer2011_1}).
Assuming that a brain section contains all possible nerve fiber configurations, the region with maximum retardation signal $|\sin\delta|_{\text{max}}$ (orange ellipse in \cref{fig:Transmittance_vs_Retardation}A) is therefore expected to contain mostly horizontal parallel fibers ($\alpha \approx 0^{\circ}$) with a high fiber density (max.\ $d\,\dn$) and thus to cause a maximum of absorption. Regions with even lower transmittance values are accordingly expected to contain steep (out-of-plane) fibers which increase the scattering and thus the attenuation of light.

By comparing the normalized transmittance values ($I_{\text{T,N}}$) of regions with small retardation values to the transmittance of the region with maximum retardation ($I_{\text{ref}} \equiv I_{\text{T,N}}(|\sin\delta|_{\text{max}}))$, the regions can be classified into three categories (see \cref{fig:Transmittance_vs_Retardation}):
\begin{enumerate}
	\item $I_{\text{T,N}} \ll I_{\text{ref}}$\,: regions with notably lower transmittance values are expected to contain steep (out-of-plane) fibers (see yellow arrows and regions surrounded by a yellow line),
	\item $I_{\text{T,N}} \sim I_{\text{ref}}$\,: regions with similar transmittance values are expected to contain flat (in-plane) crossing fibers (see cyan arrows),
	\item $I_{\text{T,N}} \gg I_{\text{ref}}$\,: regions with notably larger transmittance values are expected to have a lower fiber density (see magenta arrows).
\end{enumerate}
For regions with slightly lower or larger transmittance values, an unambiguous classification is not possible.
Provided that the region with maximum retardation has the largest tissue absorption, lower transmittance values can only be caused by steep fibers. Similar transmittance values, however, could also be caused by a small number of steep fibers, and larger transmittance values could be caused by a small number of in-plane crossing fibers (or a smaller number of steep fibers). A classification by means of retardation and transmittance values can therefore only serve as an indication of the underlying fiber configuration and should always be considered in addition to individual tissue characteristics.
As the transmittance depends on the tissue preparation, the combined analysis of transmittance and retardation should only be performed section-wise.
Brain atlases and 3D-reconstructed images (cf.\ \cref{fig:3D-Transmittance}) validate the classification of regions in  \cref{fig:Transmittance_vs_Retardation}.

\begin{figure*}[!t]
	\centering
	\includegraphics[width=1.45\columnwidth]{Fig_Transmittance_vs_Retardation}
	\caption{Combined analysis of transmittance and retardation images allowing to distinguish between brain regions with in-plane crossing and out-of-plane nerve fibers. The figure shows the normalized transmittance image ($I_{\text{T,N}}$) and the retardation image ($\vert\sin\delta\vert$) of a coronal section through the right hemisphere (occipital lobe) of a vervet brain (cf.\ \cref{fig:3D-Transmittance}(a)). The transmittance in the region with maximum retardation (orange ellipse) is used as a threshold value ($I_{\text{ref}} \equiv I_{\text{T,N}}(\vert\sin\delta\vert_{\text{max}})$). Regions with small retardation values and notably lower transmittance values ($I_{\text{T,N}} \ll I_{\text{ref}}$, yellow arrows and regions surrounded by a yellow line) are expected to contain steep (out-of-plane) fibers. Regions with small retardation values and similar transmittance values ($I_{\text{T,N}} \sim I_{\text{ref}}$, cyan arrows) are expected to contain flat (in-plane) crossing fibers. Regions with small retardation values and larger transmittance values ($I_{\text{T,N}} \gg I_{\text{ref}}$, magenta arrows) belong to regions with low fiber density, \ie, regions with a large amount of unmyelinated axons or surrounding tissue.}
	\label{fig:Transmittance_vs_Retardation}
\end{figure*}

\section{Discussion and Conclusion}
\label{sec:discussion}

Conventional bright-field transmission microscopy measurements of fibrous tissue samples provide usually only 2D information about the underlying fiber architecture. This considerably limits the application of these methods in the analysis of three-dimensional fiber structures, \eg, when studying the complex architecture of nerve fibers in the brain.
In this paper, we show both in experimental and simulation studies that the scattering of light enables a more enhanced interpretation of transmission microscopy images, providing additional structural information about the three-dimensional fiber architecture in brain tissue samples.

First, we exploited various techniques to derive three-dimensional structural information from brain tissue samples with unknown substructures.
Our experimental studies on brain sections from different species (rodent, monkey, and human, see \cref{sec:exp-studies}) have shown that the polarization-independent transmitted light intensity (transmittance) significantly decreases with increasing out-of-plane inclination angle of the enclosed nerve fibers (by more than 50\%). Using finite-difference time-domain (FDTD) simulations, we could successfully model this effect and show that the decrease in transmittance is caused by polarization-independent (isotropic) light scattering and by the finite numerical aperture of the imaging system (see \cref{sec:simulated-transmittance}).
Polarization-dependent light scattering which leads to diattenuation (polarization-dependent attenuation of light) cannot explain the observed transmittance effect because the diattenuation of brain tissue was shown to be small \cite{menzel2017,menzel2019}.

Furthermore, we could use the FDTD simulations to explain the increasing transparency of brain tissue samples with increasing time after tissue embedding (see \cref{fig:Transmittance_vs_Time}): when the embedding solution soaks into the surrounding myelin sheaths of the nerve fibers, this leads to an equalization of the effective refractive indices and thus to reduced scattering, which increases the transparency of the tissue.

Note that both measured and simulated transmittance values depend on many parameters such as the homogeneity of brain tissue or the density of nerve fibers, which are not easily accessible. As long as the exact underlying tissue structure is not known, our simulation results can therefore only serve as a qualitative prediction for the interpretation of measured data.

As the simulated samples are only characterized by their geometry and refractive indices, biological and non-biological samples with comparable fibrous structures (\eg, muscle fibers, collagen, artificial fibers) are expected to show similar transmittance effects. To increase the transmittance contrast between flat and steep fiber structures, the embedding solution should have a different refractive index than the fibers (cf.\ Fig.\ S\ref{fig:Sim_TransmittanceCurves}(a)-(b) in the Supplemental Material).

The observed transmittance effects are mostly independent of the polarization so that standard transmission microscopy techniques can be used to obtain 3D information about the underlying fiber configurations, without need to change the experimental setup or to repeat measurements. This greatly enhances the application of conventional bright-field transmission microscopy which is available in many laboratories and so far only used to gain 2D structural information.

When generating a detailed model of the nerve fiber architecture in the brain, the reconstruction of brain regions with crossing nerve fibers poses a major challenge.
With 3D-Polarized Light Imaging (3D-PLI), it is generally not possible to distinguish brain regions with in-plane crossing fibers from regions with out-of-plane fibers or from regions with low fiber densities, because they all yield low birefringence signals.
Using FDTD simulations, we could show that the transmittance of in-plane fiber configurations does not depend on the crossing angle between the fibers (see \cref{sec:sim-transmittance-crossing}).
Applying the predictions of our simulation studies to experimental data, we could demonstrate that a combined analysis of transmittance and retardation (strength of the birefringence signal) enables to distinguish between these regions (see \cref{sec:exp-sim}).
Our simulations also revealed that the transmittance can be used to detect out-of-plane fibers in regions with in-plane crossing fibers, which is not possible with current techniques.
The combined analysis of transmittance and retardation images can also be applied to past 3D-PLI measurements in order to validate and -- if necessary -- correct the reconstructed fiber orientations.

Apart from the fiber inclination, the transmitted light intensity reveals much more information about the underlying tissue structure when studying the exact pattern of the scattered light. Our simulation studies in \cref{sec:sim-transmittance-crossing} have shown that the scattering pattern can be used, for example, to identify the crossing angle of nerve fiber bundles, which is not easily accessible with current measurements. How the scattering pattern is related to the exact underlying fiber structure and tissue homogeneity will be addressed in future studies.
Major features of the scattering pattern (like the fiber crossing angle) can be determined by simply placing an aperture between light source and sample and measuring the transmitted light intensity for different positions of the aperture.

The FDTD simulations proved to be a valuable and reliable tool in many aspects: they allow to better understand the interaction of polarized light with brain tissue, to find explanations for the observed transmittance effects, to make general predictions, and to improve the measurement procedure and analysis.
In contrast to previous top-down simulation approaches of 3D-PLI that model the optical properties of the nerve fibers by series of Jones matrices (\textit{simPLI} \cite{dohmen2015,menzel2015}), the FDTD simulations solve Maxwell's equations and allow to model more complex effects like the scattering of light, but they require much more computing time.

Most nerve fibers in the brain are surrounded by a so-called myelin sheath, which consists of multiple layers with 3--5\,nm thickness (see \cref{sec:model-nerve-fibers}). If the exact layered structure of the myelin sheath is modeled, the mesh size in the simulations can be at most 3\,nm. In this case, the simulation of a single nerve fiber with 1\,\um\ diameter consumes almost 290\,000 core hours (see \cref{sec:diff-myelinlayers}). To enable the simulation of larger tissue samples with various simulation parameters, we developed a simplified nerve fiber model with double myelin layers and a simplified model for the imaging system (the incoherent and diffusive light source was modeled by monochromatic light with normal incidence). We could show that these simplified models still reproduce the observed transmittance effects and that our results are not sensitive to small changes in the simulation parameters (see \cref{sec:error-estimation} and \cite{menzel}), so our model is a good compromise between accuracy and computing time.
The developed simulation framework can easily be adapted to microscopy techniques with different optics (numerical aperture, wavelength, polarization, etc.) and to other species and tissue types.
Further brain tissue components like glial cells can easily be added to the simulation model \cite{ginsburger2019}.

In summary, we have developed and successfully applied a versatile simulation framework for transmission microscopy measurements of fibrous tissue samples that allows to study light scattering in larger samples like brain tissue, using finite-difference time-domain simulations.
We have demonstrated both in experimental and simulation studies on various brain tissue samples that the polarization-independent transmitted light intensity (transmittance) provides information about the 3D orientation of the enclosed fibers, allowing to use simple bright-field transmission microscopy to study three-dimensional fiber structures. Finally, we could show that the transmittance can be used to classify brain regions with low birefringence signals without changing the experimental setup or repeating measurements. This enables a more enhanced interpretation of three-dimensional nerve fiber architectures in the brain.

\begin{acknowledgments}
	We thank Markus Cremer, Christian Rademacher, and Patrick Nysten for the preparation of the histological brain sections, David Gr\"{a}{\ss}el and Isabelle Mafoppa Fomat for the 3D-PLI measurements, Philipp Schl\"{o}mer for generating the transmittance and retardation images, Martin Schober, Marcel Huysegoms, and Sascha M\"{u}nzing for image registration, Felix Matuschke for developing the algorithms to generate the fiber configurations, Sebastian Bludau for the bright-field transmission microscopy measurements, Andreas Wree for providing the human brain sample, and Karl Zilles and Roger Woods for collaboration in the vervet brain project.
	This work has received funding from the Helmholtz Association portfolio theme \textit{Supercomputing and Modelling for the Human Brain}, from the European Union's Horizon 2020 Research and Innovation Programme under Grant Agreement No.\ 7202070 and 785907 (\textit{Human Brain Project} SGA1 and SGA2), and from the National Institutes of Health under grant agreement No.\ R01MH092311 and 5P40OD010965.
	We gratefully acknowledge the computing time granted through JARA-HPC on the supercomputer \textit{JURECA} \cite{jureca} and \textit{JUQUEEN} \cite{juqueen} at Forschungszentrum J\"{u}lich.
	M.M. designed the study with help from M.A. and K.M., analyzed the measurements and carried out the simulations. M.M., M.A., H.D.R., and K.M. contributed to the interpretation of the data and provided theoretical considerations. H.D.R. and K.M. provided the FDTD software. I.C., L.S., and F.S.P.\ produced the TPFM measurements.
	K.A.\ contributed to the anatomical content of the study. M.M. wrote the paper with revisions from M.A., H.D.R., K.A., and K.M.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


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Survivor's Guilt. This is a phrase coined, typically, for Holocaust survivors and war veterans after going through a life-threatening event and coming out alive, if that's the correct word to use, and being able to speak about it. They usually feel the stress of survivor's guilt after losing peers or family to this event. It's not that these people are ungrateful, but thoughts, or maybe ghosts, haunt their mind causing them to ask "why not me?" Maybe they feel indebted to those that lost their lives. Maybe if their positions were switched, they would have died rather than the person who did. More likely than not, there could be a connection to survivor's guilt and post-traumatic stress disorder.
But- What if you don't have to physically be in the presence of the life-threatening event in order to suffer from survivor's guilt?
The Art of Being Haunted follows a young college student, Basqui, trying to make his way back to school after facing a traumatic event. Without revealing what happened, or what happens after, you can see his shift in personality when doing regular things such as talk to his mother, talk to a girl, or just go back to school. Ordinary things become difficult when you're constantly wondering if your life has any more meaning than the ones that lost theirs.
The beautiful thing about film is being able to take experiences and stretch the realism into surrealism.
I remember the summer of 2006 for a few reasons: I graduated high school and the blood on the street rose with the sun's heat. July of that summer, I lost a great friend, who I thought was going to thrive in life. He was way too live to die at 18. The unstoppable feeling of getting a diploma fizzled within a month when the realization that death had its own agenda came. Although I wasn't there when he was murdered, I did visit the street it happened on. I felt the reenactment in my mind. I saw him. Saw him suffer. At the funeral, I saw his body. I didn't feel the same liveliness I felt in him a few weeks prior.
If this young pitbull of a spirit can be put down so easily, what does that say about mine? Why would the universe remove someone with so much potential before me?
These were my thoughts at 17.
Basqui, whose name is taken from Jean-Michel Basquiat, is an artist. In the film, there are backdrops of murals and camera angles through his paintbrushes. There is a reason for his name and the title of the film The Art of Being Haunted. Aside from the fact that I was a graphic design major my freshman year, I think there is an art to being haunted. Our experiences color us into the beings we are today. Sometimes we have to shift the palette a bit to notice the other colors we have.
Even if you are broken, there's a mosaic still inside you. Even when your colors a broken, know there's a rainbow still inside you.
It's not easy, but it is possible. For me, going to therapy at 18 was a step to seeing the other colors in my life. My friend is dead, but I'm still alive. With that is the power to create this life however I so choose.
Shouldn't I be grateful for that?
I think we sometimes forget that life is a privilege. Out of my privilege of life, I owe him that much.
We've shown this film at schools, public theatres, and now it is available online, all with the hopes that people will be able to seek help if they find that they need it.
If you take nothing else from watching this short film, I hope you take note that Basqui does make a step to find the masterpiece within him again. You'll notice it when you see the colors.


This page is showing 74 Martial Arts Schools, Studios, Dojos & Clubs found within 10 Miles of Mount Laurel. Most of these schools offer self defense classes for children, men and women. Some may also offer After School Karate for kids. Karate, Kick Boxing, Mixed Martial Arts (MMA), Tae Kwon Do & Jiu-Jitsu (Jujutsu/Jujitsu) are the top Martial Arts offered in Mount Laurel area.
Chart based on style information available from 72 Martial Arts Schools in Mount Laurel area.
Distance is showed approximately from the downtown area of Mount Laurel, NJ. Click on 'Map' next to a Dojo to see it on the Map. To see a list of Martial Arts and Self Defense classes near you, Search with your address.
Most of these Martial Arts Studios, clubs and gyms offer Karate classes for kids or Self Defense classes for children, men and women in Mount Laurel area. If you are looking for classes or lessons near your address in Mount Laurel, please use the following search box and see a list of Martial Arts Schools, clubs and organizations near you.
See Martial Arts Schools and classes in places around Mount Laurel, New Jersey: Marlton, Mt Laurel, Moorestown, Evesham Township, Rancocas, Maple Shade, Maple Shade Township.
If you are associated with a Martial Arts School, Club or Dojo in Mount Laurel, please list it with dojos.info.


text:
The Award-Winning Brothers: A Tale Of Two Sons Comes To Switch With Exclusive Co-Op Mode
And it's out next week!
by Ryan Craddock Tue 21st May 2019
Subscribe to Nintendo Life on YouTube
Award-winning adventure game Brothers: A Tale of Two Sons is headed to Nintendo Switch, it has been confirmed. You won't have long to wait to enjoy it either, as it'll launch for the system next week.
Hugely popular amongst critics and players alike on other platforms - it's been on PS3, PS4, Xbox 360, Xbox One, PC, and more in the past - Brothers: A Tale of Two Sons has you guiding two brothers on a fairytale journey. Up until now, the game had you controlling both characters with just one controller (other versions would have you moving one brother on each control stick) but this is all about to change.
On Switch, an all-new and exclusive co-op mode will be available. This new mode will let you team up with a friend to explore the heartfelt story together. Whichever mode you choose, expect to find pretty locations, emotional sequences, and the occasional harrowing boss. The Switch version will also come with exclusive bonus content, including a behind-the-scenes commentary from director Josef Fares and a concept art gallery.
The game will launch as a digital-only release on Switch on 28th May, just a week from today, for $14.99. Anyone who pre-orders the game on the eShop will get a 10% discount.
Have you played this one on other platforms? Happy to see it arrive on Switch? Let us know if you'll be grabbing this one by leaving a comment below.
Review: Brothers: A Tale of Two Sons
Brothers: A Tale of Two Sons (Switch eShop)
About Ryan Craddock
Ryan can list the first 151 Pokémon all in order off by heart – a feat he calls his 'party trick' despite being such an introvert that he'd never be found anywhere near a party. He'd much rather just have a night in with Mario Kart and a pizza, and we can't say we blame him.
LunarFlame17
Tue 21st May 2019
Oh man, this game is real good. Not sure if I'm going to buy it again, though, because it's also very much a game where, once you've played it, you've played it, and there's no real reason to go back. But if anyone here hasn't played it yet, you really should! It's fantastic!
I suspected this would be ported to switch at some point. Day one purchase for me. Never played it but I think it was TotalBiscuit's favourite game, so I'm excited to give it a go!
Nice. I borrowed this game from a friend but never got around to playing it. Heard great things and wondered why it wasn't 2 players to begin with. I'll be picking this up for some co-op fun. Hopefully it gets a physical release on switch.
UmbreonsPapa
I got it on the 360 as Games with Gold freebie, but never finished it for whatever reason.
dethkult
Played this one on PC. Have to say one of my favorite puzzle game ever.
daveh30
Not one I'd want to double dip on, but definitely a great game. Highly recommend if you haven't played it.
N64-ROX
Pfft. Two anlalog sticks, la dee da.
Played this on iPad - the controls worked, I guess, but was not an ideal experience. Also, it crashed regularly. That all may have put me off the gameplay, which I found a little clunky, but I appreciated the fact it was trying to tell a story in an interesting way. Definitely worth a look as a kind of action-based, animated visual novel.
pinta_vodki
Huh? That defeats the whole purpose of the game though, doesn't it? I mean, controlling two brothers simultaneously was at the same time a cool game mechanic and a great thematic statement about exploring the connection between two people in a single player game. Playing the role of that connection itself, if you will. Seems like compromising the artistic vision, in a way. (But of course that's all IMO, since the developers obviously made that addition themselves, so who am I to judge.)
Switch is a great co-op machine, but I would urge people to play Brothers in single-player to experience the game as it was conceived.
gcunit
I feel like this game gets too much credit for the 'controlling the two brothers at once' mechanic and theme. I mean it was reasonably novel, and it looks nice, but it's over in a blink of an eye and has very little replayability from what I can remember.
hakjie11
a good game but a very short one
Bomberman64
Now we just need Dunkey to do a review of it.
AlexSora89
Wait, wasn't this game the one with Game Boy graphics in it?
I vaguely remember a game titled like that... "Brothers", "Two Brothers" or something.
ThatNyteDaez
Way back on Ps3 (I think it was) I played through the entire game with my bestie. We both had one half of the controller the entire time and that was basically it. It didn't take long and we went from start to finish together.
I can't imagine the "co-op" mode being much different. So I'm not sure why its being added unless there's a whole new story to it.
JLPick
A great game on the PS4 that I greatly enjoyed, the scenery was fantastic and the plot was pretty decent too, but not one that I'd double dip on, unless the price was right for it (and for me, $10 or less, and I know it won't be that price). Guess I'll wait for it to go on sale...hopefully it's getting a physical release.
BlueBlur101
@Bomberman64 "Who would play this stupid-ass game"
gets rejected by Microsoft despite working within guidelines of critique
Another wishlist item down to be reborn on another wishlist. Lord knows how many times I've been on the verge of getting it on Steam or HB - and even on Google Play at times (the sight of an onscreen digital "joystick" in the screenshots tends to be a strong demotivator for me, though). But a Switch version is a Switch version - and this one packs some neat extras to boot!
I forgot about this game! Almost bought it for pc. Now I wait for the switch. This is one good game.
I remember being interested in this game on PS3... until I found out that it DIDN'T have local co-op... how stupid.
Not that it does, I will likely get it on Switch.
vanYth
Really great but short game. Finished it two times on PS3, so will skip it here.
Beermonkey
If I hadn't of already played and completed this on other consoles would be all over it. Highly recommended for anyone who hasn't played it.
Ladasta
Agree with the Beermonkey. Played this one many years ago on ps3. If I hadn't I would probably buy it now.
FiveDigitLP
Great game. I DEFINITELY recommend it! It's got an emotional story (yet has no voice acting) and has a unique gameplay hook much like what @pinta_vodki says above. It's fairly short, but worth it regardless.
Decent game, A Way Out is a bit better. I wouldn't mind that on the Switch at some point. Blur the nudity or something.
Aurumonado
I love this game. I've been waiting for a switch port for a while! I'll get the inevitable physical edition from super special reserve hidden boutique games!
adh56
I really liked what I played of this on PS4. It truly is something to wrap your head around controlling each brother with an analog stick each and the shoulder buttons. I'll get in on that prepurchase price
Wed 22nd May 2019
@Tangerine THAT is all the recommendation I need. If it was good enough for TB to call it his favorite game, I am very interested!
This could be the game that my wife and I are looking for. She's a very novice gamer, as in doesn't really game at all but lover reading novels. I keep trying to explain that I love games and RPGs because of the story, and when it's done well it's an interactive novel. Hope this one bridges the gap for us.
SwitchForce
No more eShop have both options.
It's a great game, but I feel like adding actual co-op misses the point of the experience.
@holygeez03 Controlling both brothers is what makes this game work. I think co-op will lessen it.
You only need the sticks and the bumper and trigger buttons for this game anyway. It's no different from a twin-stick shooter in control complexity.
Feature: Nintendo Switch Ports We'd Love To See In 2020
We ain't beggin'
Starbreeze Studios
Adventure, Puzzle
28th May 2019 (US/Canada), $14.99
28th May 2019 (UK/EU/AU), £9.99
Review: Brothers: A Tale Of Two Sons - A Welcome Return Of An Indie Classic
Nintendo Download 30th May (Europe)
Thu 30th May 2019
Review Brothers: A Tale Of Two Sons - A Welcome Return Of An Indie Classic
Brothers A Tale of Two Sons
Nintendo Download 23rd May (North America)
Thu 23rd May 2019

redpajama_set_name: RedPajamaCommonCrawl


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77 943 messages and 7 074 likes sent during the past 3 hours and 54 minutes.


text:
Home → Instagram
TCN Admin — July 2, 2019 in Instagram
Instagram is a popular online social media platforms to share photos and videos. This Facebook-owned platform has more than a BILLION monthly active users. Everyone on Instagram wants to be…
Instagram Now Lets you to Apply for Blue Tick Verification, Here is How You Can Apply
TCN Admin — September 3, 2018 in How to
Instagram with 400 million active users, it becomes necessary to keep a tab on security while giving the best experience to the users. In a recent announcement, Instagram has started…
How to Post Pictures on Instagram from Your Windows and Mac Laptop Computers
TCN Admin — August 30, 2018 in How to
With over 400 million active users worldwide, Instagram is one of the most popular social network sites. This platform is owned by Facebook it is very different that Facebook in…


text:
Home Politics & Government Tammy Baldwin announces she'll vote to pass 'new NAFTA'
Tammy Baldwin announces she'll vote to pass 'new NAFTA'
Senator says Democratic modifications led to 'a better trade deal that I can support'
Pres. Trump participates in USMCA signing ceremony, Nov. 30 2018 (Photo courtesy US Dept of State)
Parting company with her Congressional successor, Sen. Tammy Baldwin (D-Wisconsin) Tuesday announced she plans to vote to ratify the new United States Mexico Canada Agreement (USMCA).
Sen. Tammy Baldwin
"President Trump's trade wars have hurt our Wisconsin economy and more than 1,900 dairy farms have gone out of business since he took office," Baldwin said in a statement issued late Tuesday, after the Senate Finance Committee endorsed the agreement in a bipartisan vote.
"The President's deal with Mexico and Canada fell short but I support the improvements Speaker Pelosi and House Democrats won to make this a better trade deal that I can support," Baldwin stated.
The implementing legislation for the agreement — nicknamed "the new NAFTA" for the North American Free Trade Agreement that it replaces — "includes many changes I have pushed for with the Trump administration," Baldwin said, "including truly enforceable labor standards that benefit our workers, and making sure that we confront Canada's unfair trade barriers and Mexico's limits on Wisconsin cheese exports so that we have a trade deal that increases market access for our Wisconsin dairy farmers and cheesemakers."
Baldwin, a member of the U.S. House of Representatives from 1999 until her election to the Senate in 2012, pointed out that when the original NAFTA was ratified in 1994 (she was a member of the Wisconsin Assembly at the time), she opposed it because it "cost Wisconsin jobs and needed to be fixed." She continued: "I will vote for the USMCA because it is a better deal for farmers, manufacturers, businesses and workers."
The agreement that went to Congress last year, where it passed the House of Representatives in late December, was the result of negotiations that included Democratic House Speaker Nancy Pelosi, Sen. Sherrod Brown (D-Ohio) — seen as a strong labor ally — and the AFL-CIO, the nation's largest labor federation. Some other union groups remained opposed to the re-negotiated agreement.
U.S. Rep. Mark Pocan (D-Black Earth), who succeeded Baldwin in Congress, was the only member of the Wisconsin congressional delegation to vote against it in the House of Representatives.
U.S. Rep. Mark Pocan
While Pocan agreed that Democratic negotiators had "made this new deal better" with improved labor standards and enforcement mechanisms and by removing language extending pharmaceutical patents, he said in a statement after his vote that it didn't go far enough.
"I cannot be confident that this trade deal would heal the wounds inflicted by NAFTA, including rampant outsourcing of American jobs, the closing of factories and manufacturing facilities across the country, and decades of harm to working and middle-class communities," Pocan stated. "The deal also fails to take a once in a generation opportunity for North America to take bold, collective action to address the climate crisis that threatens the future of our entire planet."
In a recent Wisconsin Examiner commentary, retired Wisconsin farmer Jim Goodman and University of San Francisco economist Anthony Pahnke also criticized the revised trade agreement's labor and agriculture provisions as inadequate to protect worker rights or the interests of farmers while favoring agribusiness giants.
Baldwin's statement endorsing the agreement focused on securing perceived gains for the state's dairy industry, while it also served as a rebuff to the Trump administration's use of trade-war tactics: tariffs on foreign goods that have triggered counter-tariffs and penalized American farmers and manufacturers.
"Going forward, President Trump needs to understand Wisconsin needs better trade deals, not trade wars," Baldwin stated, "and that in order to stop the outsourcing of manufacturing jobs we not only need fair trade deals, our workers need tax reform that rewards their hard work and doesn't encourage corporations to send their jobs to other countries."
Mark Pocan
NAFTA 2.0
Tammy Baldwin
Standing up for peace and compassion
U.S. House votes to torpedo DeVos student loan rule


text:
Artist uses murals to celebrate Latinx culture in one of the most segregated cities in America
Mauricio Ramirez uses his art to highlight his culture
I think our culture is pretty beautiful and stuff, and I think it's really cool to see how much of an impact that we've had, you know, in this Milwaukee community, my family has deep roots here since, like the forties and thirties. And that's something that I always considered. They came over by way of railroad and, you know, kind of helped build some of the tanneries here. Try to use, like every single color in the rainbow, my murals. But mainly I tryto give my murals from Seoul by kinda seeing ourselves on the walls and stuff. It's kind of like a reminder that, you know, we're important.
"I think our culture is really beautiful and it's really cool to see how much of an impact we've had in the Milwaukee community," says artist Mauricio Ramirez. He uses his art to highlight his culture in one of the most segregated cities in America: Milwaukee, Wisconsin. Originally from Mexico, his family immigrated to the United States has deep ties to the city. "My family has had deep roots here since the '40s and '30s, and that's something that I always consider," he says. "They came over by railroad, and kind of helped build some of the tanneries here."Ramirez has been working on murals throughout the city, like this one for Marquette University. "I try to use every single color in the rainbow on my murals, but mainly I try to give my murals some soul."
MILWAUKEE —
"I think our culture is really beautiful and it's really cool to see how much of an impact we've had in the Milwaukee community," says artist Mauricio Ramirez.
He uses his art to highlight his culture in one of the most segregated cities in America: Milwaukee, Wisconsin.
Originally from Mexico, his family immigrated to the United States has deep ties to the city.
"My family has had deep roots here since the '40s and '30s, and that's something that I always consider," he says. "They came over by railroad, and kind of helped build some of the tanneries here."
Ramirez has been working on murals throughout the city, like this one for Marquette University.
"I try to use every single color in the rainbow on my murals, but mainly I try to give my murals some soul."


Industry and public opinion was strongly against the proposed change, citing safety as the major concern. The consultation's premise that extending the grace period would also save motorists money was also proved false.
"This is a victory for common sense. In our response to the consultation, we strongly argued that MOT is a necessary and affordable safety check that plays a vital role in keeping our roads amongst the safest in the world. Together with colleagues from all corners of the automotive aftermarket, we presented clear evidence that extending the grace period to four years would have a detrimental impact, so it's right the DfT has listened.
Micheldever Group is the second largest independent wholesaler, distributor and retailer of tyres in the UK, selling six million tyres nationwide. It is responsible for one in five replacement tyres sold in the UK.


This week on Puhr News! Dealing with the major news of this week the USMCA (NAFTA was easier to say) and the Kavanaugh & Ford hearings last Thursday. Andrew also rants about the pointless spectacle and danger of over the top Gender Reveals, and how HIV can stop Cancer.
Like Puhr News on Facebook!
Foodies Watching Movies S3 E5 - Gobble Gobble!
Adulting Ain't Easy 014 - Thanksgiving!!
Journey Into Comics 218 - Excelsior!


I'm a NY trainer who's been barefoot or in my Altras for months and now looking for a winter trail shoe that can cross over as a city shoe in bad weather so I can travel light, dry and warm. Any updated ideas for winter 2014/2015?
I'm training for a marathon, and my kids (age 8 and 6) will be training for a kids version, where they'll run in various increments up to the race day and they'll complete the 26.2 mile on the finish line. My kids are athletic, but have never had running shoes just for that purpose. Any recommendations?
I've been walking in minimalist shoes for two years now, and also done some running with barefoot shoes on roads and gravel roads - only short runs - 2 to 5 miles, but still, I thought that I had developed some foot strength.
So this spring I started trail running, and loved it. Only 2 miles to begin with, but then I had two longer runs - and now my left foot hurts. The top of the foot, towards the outside of the foot (the 4th and 5th metatarsal if I have got the technical language right.) A dull ache, which is better when I've warmed up and walked/run for a bit, but hurts more after rest and in the morning.
I've been running in pretty minimal shoes. ZEM 360s on treadmill, Inov-8 bare-x light 150 on roads, and Inov-8 trail roc 150 on trails.
I've taken it easy for a few weeks now, and it gets better, but is still there.
So - it seems that I underestimated the strain of trail running with such a minimal shoe as the trail roc 150, and also the difference between gravel roads and uneven trails.
I'm asking for tips here: should I just lay off running - at least trail running for a while?
Or can I start running again, but very short distances?
So - A complex question, but I'm sure there are some people out there that can answer parts of it!
We are interested in knowing some of the lessons the kids are learning win it comes to facing challenging circumstances and using them as a learning experience. What slogans or statements do the kids make now that help them get through their fears and how have you as parents even grown from them.
We are dying to know if Brienne went with tenacious bling or rainbow dash.
I read the blog here by googling the BIOM Lite and then I realized that I am entering a new world. I am now so interested of becoming a barefoot walker. My feet and legs are not strong. If I stand in the subway car for more than 30mins, my feet will feel pain. I want to practice my feet. Will you please recommend a pair of shoes as my first minimalist shoes? On my way to the work, I have to walk for about 20 mins and then take 40 mins subway, mostly stand in the car. Do you think it is a good idea to ware a shoes like that? e.g. the BIOM Lite/Grip or OTZ300GMS? thank you for your help.
Is there a particular brand/type that you would recommend for someone new to minimalist footwear? I'm not looking for anything for running as I have another injury. I'm looking for something that would be good for every day use and a few short walks a week.
What if I can't wear minimalist shoes all the time?
I climb for the electric company and we are required to weara bout that has a very high heel and metal shank for support when climbing. But I have been wearing my kso's and vivo and love it my question is will wearing these boots 40 hrs a week and my minimalist shoes the rest of the time cause any health problems for me/my feet?
Hi everyone, I started my "barefoot revolution" last spring and had the best summer I ever had in a long time! My back, my knees, my whole body thanked me for it. My feet even grew by half a size! I need to say that I'm a walker, not a runner. Then winter arrived (I'm up here in Ottawa) and I needed to get winter boots. I got something really warm, Keen boots, but ever since I started wearing them my lower back hurts like a $!% (I'll let you guess). I couldn't really find a casual winter solution for minimalist enthusiasts who needs to commute to go to work. I found the Scott Mens from Vivobarefoot but as all there footwear, they were sold out. Does anyone have any other suggestions or do I need to wait for them to become available?
I also use a Steripen Freedom, but haven't done a large through hike like you guys are planning. How are you going to recharge the battery while on the trail?
I'm assuming you'll have backup water purification.
I am in the market for a minimalist shoe that is very durable and will stand up to off-trail use. Any suggestions?
I work in a warehouse environment and am looking for a good shoe to wear daily. I have previously purchased a pair or Lems/Stems and the sole began to come apart from the shoe only after two weeks of wearing them for normal daily activities. They were kind enough to send me a replacement pair, but they did the same thing.
Looking for info on a wide shoe that offers a decent casual look but won't fall apart while standing still. I've never owned any Vivo shoes, are they pretty durable?
Minnesota winters are a bit brutal.
I am looking for a closed toe minimalist shoe that i can wear at work (a kitchen) and also at my martial arts dojo where they require shoes. May i please have your opinion on the matter? I am thinking; something that looks pretty casual, a good grip would be a plus, wide toe box, durable enough the kick wooden dummies repeatedly (and secure enough not to slip off), laces (or something equally flat on top so nothing digs into my foot while kicking), and a thin sole. So far i like the (look of) Feelmax Aapa and Lems Primal. Any advice/suggestions would be most appreciated. Thank you!
Yes, they are renfair shoes. But several of the styles are perfectly normal for daily wear and are made of daily wear. They have a few that women could get away with in most offices, plus one short boot called the Villager that men could wear on most occasions. Also another one called the buckle boot that men could wear to nearly every thing.
What can men wear when running shoes won't do? Women can usually find some variation of ballet slipper without too much work, but its different for men. A man's work shoe is hard to find.
They will let you have your choice of soling, including just plain leather because they make to order.
I intend to buy from them very soon.
wading boot for stockingfoot waders?
I'm a stream ecologist, and wear Simms stockingfoot waders for my field work. There's a lot of hiking up and down streams, and bushwhacking, and the wading boots I wear over the waders just kill my feet. Frankly, they're dangerous - they're so stiff that I can't tell what I'm stepping on and I've had some close calls.
I'd love to have something lighter and more flexible. Any suggestions? They need to keep dirt out; I don't want bits of grit getting in and chewing holes in my expensive waders! At the same time, water needs to be able to drain out of them. Also they need laces to hook gaiters onto; more keeping gravel out.
I considered neoprene kayaking booties, but the wader feet are neoprene - I don't really fancy hiking with two layers of neoprene over my feet! They're warm enough as it is. The gaiters are neoprene as well. Fantastic for cold-season work (which I do quite a bit of) but not so great for hiking into a site on a hot day.


text:
A timeline for Latin.
Created by Walker ⟶ Updated 1 months ago ⟶ List of edits
Cicero gives his speech to Catiline.Lucius Opimius: Roman consul who ordered the death of 3,000 supporters of Gaius Gracchus.Marcus Flaccus: Elected consul in 125 B.C. He was an ally of Gaius Gracchus.Gaius Marius: Consul of Rome who worked closely with the tribune Saturninus.Valerius Flaccus: Roman consul along with Marius. Sided with Sulla during the Roman civil war and eventually became a dictator.Gaius Servilius: A Roman politician who is regarded as a hero because he killed a peasant who was trying to become king.
Gaius Gracchus: A Roman politician who was forced to commit by Lucius Opimius in 121 BC.Lucius Saturninus: Roman tribune who strongly advocated that veterans of the Cimbric wars were granted land. He died in 99 B.C. when he was stoned to death in the senate-house where he was hiding.


text:
package consumer.domain;

import java.util.Random;

import com.fasterxml.jackson.annotation.JsonIgnore;

public class PhoneMessage {
	// must begin with a plus symbol followed by 1 to 9, then 1 to 14 digits (0-9)
	private static final String VALID_PHONE_NUMBER_REGEX = "\\+[1-9]\\d{1,14}";

	private Long id;
	private String telephoneNumber;

	public PhoneMessage() {
	}

	public PhoneMessage(Long id, String telephoneNumber) {
		this.id = id;
		this.telephoneNumber = telephoneNumber;
	}

	public PhoneMessage(String telephoneNumber) {
		this.id = getRandomId();
		this.telephoneNumber = telephoneNumber;
	}

	public Long getId() {
		return id;
	}

	public void setId(Long id) {
		this.id = id;
	}

	public String getTelephoneNumber() {
		return telephoneNumber;
	}

	public void setTelephoneNumber(String telephoneNumber) {
		this.telephoneNumber = telephoneNumber;
	}

	@JsonIgnore
	public boolean isValidNumber() {
		return telephoneNumber.matches(VALID_PHONE_NUMBER_REGEX);
	}

	@JsonIgnore
	private Long getRandomId() {
		Random random = new Random();
		String s = "";
		for (int i = 0; i < 10; i++) {
			s = s + random.nextInt(10);
		}

		return new Long(s);
	}
}

redpajama_set_name: RedPajamaGithub


Klosterneuburg Monastery can look back on over nine hundred years of history. We warmly invite you to get to know the Monastery in both its religious and secular diversity.
At Austria's oldest winery, one can uniquely experience the connection between a centuries-old wine-growing tradition and the most modern winery technology.
The Klosterneuburg Monastery winery is the oldest wine-growing estate in Austria.