\documentclass[a4paper]{article}

\usepackage{caption}
\usepackage{csquotes}
\usepackage[acronym]{glossaries}
\usepackage{hyperref}
\usepackage[utf8x]{inputenc}
\usepackage{siunitx}
\usepackage{todonotes}

\makeglossaries{}
\newacronym{cis}{CiS}{Cells in Silico}
\newacronym{cpm}{CPM}{Cellular Potts Model}
\newacronym{ecm}{ECM}{Extracellular Matrix}
\newacronym{fem}{FEM}{Finite Element Method}
\newacronym{lbm}{LBM}{Lattice Boltzmann Model}
\newacronym{mcs}{MCS}{Monte-Carlo Step}
\newacronym{nastja}{NAStJA}{Neoteric Autonomous Stencil code for Jolly Algorithms}

\begin{document}

\title{Research Summary}
\author{Paul Brinkmeier}
\date{June 2023}
\maketitle

\section{\acrfull{ecm}}

For an extensive overview, see \cite{frantz2010}.

\begin{itemize}
	\item The \acrshort{ecm} constitutes the non-cellular parts of all tissues.
	\item It consists of:
	\begin{itemize}
		\item Fibrous proteins, most importantly collagen, elastin and fibronectin.
		\item Up to 30\% collagen.
                      Forms fibrils and fibers of different sizes which can \enquote{stick together} to make up networks.
		      There are a bunch of different collagen types.
		\item Proteoglycans, which fill the interstitial space in the form of a hydrated gel.
	\end{itemize}
	\item Cells move through and remodel their \acrshort{ecm}, which in turn changes their behavior. \\
	      $\implies$ \emph{in silico} models need to take this into account.
	\item Different tissues have different \acrshortpl{ecm}.
\end{itemize}

\subsection{Properties of the Extracellular Matrix}

Our approach takes a macroscopic view of the \acrshort{ecm}.
Individual fibrils/fibers should not be modeled.
Nevertheless we include some microscopic properties.

\begin{itemize}
	\item \textbf{Stiffness}: Matrix stiffness has an effect on tumor gowth, e.g. \cite{levental2009}.
	Measured using Young's modulus/elastic modulus $E$ which is given in \si{\giga\pascal}.
	\item \textbf{Viscoelasticity}: Creep, Stress relaxation (see below), $E$, $\eta$
	\item \textbf{Pore size}
	\item \textbf{Density}
\end{itemize}

\subsection{Viscoelasticity}

\todo{What is viscoelasticity? Show some graphs and \enquote{oral} explanation}

\begin{itemize}
	\item \textbf{Creep}:
	\item \textbf{Stress relexation}:
\end{itemize}

Generally modeled using differential equations involving the elastic modulus $E$, viscosity $\eta$, stress $\sigma$ and strain $\epsilon$.
\cite{roylance2001} mentions these constitutive models:

\begin{itemize}
	\item Maxwell: Viscous flow on the long timescale, but additional elastic resistance to fast deformations (e.g. silly putty, warm tar).
	      Does not describe creep or recovery.
	\item Kelvin-Voigt: Does not describe stress relaxation.
	\item Zener/Standard linear solid: Models creep and stress relexation.
\end{itemize}

The Lethersich and Jeffreys models are models for viscoelasticity that specifically model fluids.

\subsection{Rheology and Materials Science of the \acrshort{ecm}}

\cite{frantz2010} mentions Matrigel and collagen type I gels, so we will focus on these.

Great review with great figures: \cite{chaudhuri2020}.

\begin{itemize}
	\item \cite{sherman2015} lists the elastic modulus of collagen structures at different scales, see \autoref{fig:sherman2015-table1}.
	\item \cite{puxkandl2002} defines a model for the viscoelasticity of collagen.
	\todo{expand, give actual values}
	\item \cite{slater2017} discusses properties of Corning® Matrigel®.
	\begin{itemize}
		\item Lists elastic moduli for different concentrations and mixtures involving collagen type I around $10^1$ to $10^3$ \si{\pascal}.
		\todo{This seems very low; investigate sources}
		\item This paper shows the viscuous component in the graphs but doesn't really go into it.
	\end{itemize}
	\item \cite{aisenbrey2020} discusses alternatives to Corning® Matrigel®.
	\item \cite{sheu2001} experimentally investigate the elastic and viscous moduli of collagen gels.
	      They find that the Kelvin-Voigt model can be used to model their viscoelastic behavior.
\end{itemize}

\begin{figure}[h]
	\includegraphics[width=\textwidth]{figures/sherman2015-table1}
	\caption{Comparison of Young's modulus of collagen at multiple hierarchical levels. From \cite{sherman2015}.}.
	\label{fig:sherman2015-table1}
\end{figure}

Since viscoelastic behavior is inherently time-dependent, it will be a challenge to choose a sensible time step resolution for the model.

\section{\acrfull{cpm}}

\todo{cites}

\begin{itemize}
	\item The \acrshort{cpm} is a grid-based Monte-Carlo simulation for cells.
	\item Each cell consists of many voxels.
              These voxels contain its cell ID.
	\item In each \acrfull{mcs}, a random voxel copies the cell ID of its neighbor.
	\item The hamiltonian $H$ gives the energy of a generation. It depends on the volume and surface of cells and their reciprocal adhesion.
	\item A \acrshort{mcs} is always accepted if it reduces $H$.
              If it does not reduce $H$, it is accepted probabilistically.
\end{itemize}

\section{\acrshort{nastja} \& \acrshort{cis}}

\begin{itemize}
	\item \acrfull{nastja} is a massively parallel stencil code solver based on OpenMPI \cite{berghoff2018}.
	\item \acrfull{cis} is an implementation of the \acrshort{cpm} in \acrshort{nastja} \cite{berghoff2020, herold2023}.
\end{itemize}

\section{Models of Viscoelastic Materials}

\subsection{Chopard (Cellular Automaton)}

\subsection{\acrfull{lbm}}

\begin{itemize}
	\item A general-purpose model of hydrodynamics discrete in time and space.
	\item Discretisation in space makes it possible to calculate \acrshort{lbm} time steps using stencil codes.
	\item Extensive literature exists including implementation details, e.g. \cite{krueger2017}
	\item Can be used to model viscoelasticity, e.g. \cite{giraud1998, malaspinas2010, ispolatov2002}
	\item Probably not that simple to model matrix porosity.
	\todo{Elaborate}
\end{itemize}

\section{\acrshort{ecm} Models in the \acrshort{cpm}}

Reviews: \cite{liedekerke2015, guo2022}

\todo{Elaborate a bit}

\subsection{\acrshort{ecm} as a Cell}

\begin{itemize}
	\item Simple idea: Model \acrshort{ecm} as a special cell, i.e. a set of voxels.
	\item Set properties of the \acrshort{ecm} \enquote{cell} such that the model makes sense.
	\item Can model simple interactions such as matrix decomposition and deposition
	\item Can't really model matrix strains and deformation
\end{itemize}

E.g. \cite{rubenstein2008, scianna2013, herold2023}

\subsection{Substrate Strain \acrshort{fem}}

\cite{rens2017}

\subsection{Discrete Fiber Networks}

\todo{expand}

See papers cited in \cite{guo2022}, e.g. \cite{abhilash2014}.

\subsection{Molecular Dynamics Bead-Chain Model}

\cite{tsingos2022}


\clearpage


\section{Glossary}

\printglossary[type=\acronymtype]

\bibliographystyle{acm}
\bibliography{references}

\end{document}
