\section{Intro}

\begin{frame}{NAStJA: An MPI Stencil Code Solver}
\begin{figure}
	\includegraphics[width=0.8\textwidth]{nastja.png}
\end{figure}

\begin{itemize}
	\item CiS uses NAStJA under the hood
	\item NAStJA is a massively parallel stencil code solver \\
	      $\implies$ CiS extensions should be stencils
\end{itemize}
\end{frame}

\begin{frame}{ECM Viscoelasticity:\\A Factor in Cell Behavior}
\begin{figure}
	\includegraphics[width=0.48\textwidth]{ecm-cells.png}
\end{figure}

\begin{itemize}
	\item Collagen networks in the ECM  mechanically restrict cells
	\item Collagen networks are \emph{viscoelastic}
	\item ECM viscoelasticity influences cell behavior
\end{itemize}
\end{frame}

\section{ECM Model}

\begin{frame}{Modeling ECM Mechanics in CiS}
How can we model ECM mechanics in CiS?

\vfill{}

Two main requirements:

\begin{itemize}
	\item Model exhibits viscoelastic properties
	\item Model can be implemented as a stencil in NAStJA
\end{itemize}
\end{frame}

\begin{frame}{ECM Models in Literature}
\begin{figure}
	\includegraphics[width=0.64\textwidth]{models.png}
\end{figure}

\begin{itemize}
	\item A host of different ECM models exist
	\item Various foci, e.g. mechanics, growth factors
	\item Various approaches, e.g. FEM, Molecular Dynamics
\end{itemize}
\end{frame}

\begin{frame}{My Approach}
Two main requirements:

\begin{itemize}
	\item Model exhibits viscoelastic properties
	\item Model can be implemented as a stencil in NAStJA
\end{itemize}
\end{frame}

\section{Methods}

\begin{frame}{Lattice Boltzmann Method}
\begin{figure}
	\includegraphics[width=0.6\textwidth]{lbm.png}
\end{figure}

\[
f_i(\mathbf{x} + \mathbf{c}_i, t + 1) = f_i(\mathbf{x}, t) - \frac{1}{\tau} (f_i(\mathbf{x}, t) - f_i^\text{eq}(\mathbf{x}, t))
\]

\begin{itemize}
	\item Discretized particle velocities per lattice site
	\item Update Step: Streaming + Collision
	\item Usually used for hydrodynamics
\end{itemize}
\end{frame}

\begin{frame}{Elastic Lattice Model}
\begin{columns}
\column{0.35\textwidth}
\begin{figure}
	\includegraphics[width=\textwidth]{elm.png}
\end{figure}

\column{0.65\textwidth}
\[
\mathbf{F}_{ij} = \mathbf{r}_{ij} K_{ij} (\mathbf{u}_{ij} \cdot \mathbf{x}_{ij}) + \frac{c \mathbf{u}_{ij}}{|\mathbf{x}_{ij}|^2} + \eta \mathbf{v}_{ij}
\]

\begin{itemize}
	\item A square lattice based discrete particle method
	\item Each lattice site represents a particle
	\item Particles are connected to neighbors by springs
\end{itemize}
\end{columns}
\end{frame}

\begin{frame}{My Approach}
Two main requirements:

\begin{itemize}
	\item Model exhibits viscoelastic properties \checkmark{}
	\item Model can be implemented as a stencil in NAStJA \checkmark{}
\end{itemize}

\vfill

Challenges:

\begin{itemize}
	\item How do we integrate the model with the CPM?
	\item How can it be implemented in NAStJA?
	\item How do we make it fast?
\end{itemize}
\end{frame}

\begin{comment}
\section{Intro}
\subsection{Subsection 1.1}
\frame{
\frametitle{Example slide A}
\begin{itemize}
\item PCM, Citation: \cite{dh76,kl07} %\language
\pause
\item Bullet point 2
\item \dots
\end{itemize}
}
\subsection{Subsection 1.2}
\frame{
\frametitle{Example slide B}
\begin{block}{Block 1}
\begin{itemize}
\item Test: �������
\pause
\item Bullet point 2
\item \dots
\end{itemize}
\end{block}
}
\section{Section 2}
\frame{
\frametitle{Example slide C}
\begin{exampleblock}{Example 1}
\begin{itemize}
\item Bullet point 1
\pause
\item Bullet point 2
\item \dots
\end{itemize}
\end{exampleblock}
}
\frame{
\frametitle{Example slide D}
\begin{alertblock}{Alert 1}
\begin{itemize}
\item Bullet point 1
\pause
\item Bullet point 2
\item \dots
\end{itemize}
\end{alertblock}
}
\end{comment}
