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@ -2,11 +2,14 @@
\usepackage[utf8]{inputenc} \usepackage[utf8]{inputenc}
\usepackage[style=numeric]{biblatex} \usepackage[style=numeric, sorting=nyt]{biblatex}
\usepackage[acronym, nomain]{glossaries} \usepackage[acronym, nomain]{glossaries}
\usepackage{hyperref} \usepackage{hyperref}
\usepackage{todonotes} \usepackage{todonotes}
% Suppress notes exported from Mendeley in bibliography
\AtEveryBibitem{\clearfield{note}}
\addbibresource{references.bib} \addbibresource{references.bib}
\makeglossaries{} \makeglossaries{}
@ -31,40 +34,42 @@
\section{Introduction} \section{Introduction}
Computational models of cell behavior can be useful to simulate and reiterate experiments. Computational models of cell behavior can be useful to simulate and reproduce experiments.
In addition, they can show us how well our understanding models reality. In addition, they can show us how well our understanding models reality.
A popular approach is the \acrfull{cpm}, where each cell is modeled as a set of connected pixels or voxels on a two- or three-dimensional lattice. A popular approach is the \acrfull{cpm}, where each cell is modeled as a set of connected pixels or voxels on a two- or three-dimensional lattice.
To simulate biological processes involving thousands of cells, large lattices are needed. To simulate biological processes involving thousands of cells, large lattices are needed.
Due to the local nature of the computations involved, the \acrshort{cpm} lends itself well to distributed programming. Due to the local nature of the computations involved, the \acrshort{cpm} lends itself well to distributed programming.
We will base our work on \acrfull{cis}, which is an implementation of the \acrshort{cpm} based on the \acrfull{nastja} framework.
In order to be true to \emph{in vivo}/\emph{in vitro} findings, such \emph{in silico} models must take into account a multitude of factors influencing cell behavior. In order to be true to \emph{in vivo}/\emph{in vitro} findings, such \emph{in silico} models must take into account a multitude of factors influencing cell behavior.
One such factor is the interaction with the \acrfull{ecm} that cells exist in. One such factor is the interaction with the \acrfull{ecm}, the structural scaffold which cells are embedded in.
In this work we will focus on the viscoelasticity of the collagen networks in the \acrshort{ecm}. In this work we will focus on the viscoelasticity of the collagen networks in the \acrshort{ecm}.
We explore models of viscoelasticity that, similar to the \acrshort{cpm} itself, employ local interactions to model global effects. We will explore models of viscoelasticity that, similar to the \acrshort{cpm} itself, employ local interactions to model global effects.
In this manner the simulations remain parallelizable. This is required to fit the implementation into the \acrshort{nastja} framework so that it can be seamlessly integrated with \acrshort{cis}.
Additionally, we investigate the performance of our model using different implementations on both \acrshort{cpu}s and \acrshort{gpu}s. Additionally, we will investigate the performance of our model using different implementations on both \acrshort{cpu}s and \acrshort{gpu}s.
\section{Research} \section{Research}
\subsection{The \acrfull{cpm}} \subsection{The \acrfull{cpm}}
The \acrshort{cpm}~\cite{graner1992} models cells as sets of sites on a square lattice which are usually connected. The \acrshort{cpm}~\cite{graner1992} models cells as sets of connected sites on a square lattice.
Each lattice site is assigned the integer cell ID of the cell it belongs to. Each lattice site is assigned the integer cell ID of the cell it belongs to.
The behavior of the cells is regulated by the Hamiltonian $H$, which represents the energy of a particular lattice. The behavior of the cells is regulated by the Hamiltonian $H$, which represents the energy of a particular lattice.
The Hamiltonian contains at the least a term for the adhesion between cells on the lattice, but can be extended by other terms such as cell volume or alignment. The Hamiltonian contains at the least a cell-cell adhesion and cell volume, but is usually extended by other terms such as cell surface or alignment.
To advance the \acrshort{cpm}, a \acrfull{mcs} is performed: To advance the \acrshort{cpm}, a \acrfull{mcs} is performed:
The cell ID of a random lattice site is changed to the cell ID of one of its neighbors and the difference in energy $\Delta H$ is calculated. The cell ID of a random lattice site is changed to the cell ID of one of its neighbors and the difference in energy $\Delta H$ is calculated.
The update is always accepted if the energy decreases. The update is always accepted if the energy decreases.
If the energy does not decrease, the update is accepted probabilistically, where greater increases are less probable. If the energy does not decrease, the update is accepted probabilistically (e.g.\ by the Metropolis criterion), where greater increases are less probable.
Repeated \acrshortpl{mcs} minimize $H$. Repeated \acrshortpl{mcs} minimize $H$.
From an implementor's perspective, the \acrshort{cpm} has a great advantage over other approaches to cell simulation such as agent-based modeling: From an implementor's perspective, the \acrshort{cpm} has a great advantage over other approaches:
Since updates happen on a square lattice and changes in energy can be calculated locally, it lends itself well to distributed programming. Since updates happen on a square lattice and changes in energy can be calculated locally, it lends itself well to distributed programming.
\acrfull{cis}~\cite{berghoff2020} is a parallel implementation of the \acrshort{cpm} based on the \acrfull{nastja} framework~\cite{berghoff2018}. \acrfull{cis}~\cite{berghoff2020} is a parallel implementation of the \acrshort{cpm} based on the \acrfull{nastja} framework~\cite{berghoff2018}.
\acrshort{nastja} offers an abstraction layer for implementing stencil codes on the \acrfull{mpi}, making it possible to leverage large-scale parallelism for \acrshort{cis}. \acrshort{nastja} offers an abstraction layer for implementing stencil codes using \acrfull{mpi}, making it possible to leverage large-scale parallelism for \acrshort{cis}.
\acrshort{nastja} divides the domain into blocks, computing each stencil locally, then performing an halo exchanges of the border regions. \acrshort{nastja} divides the simulation domain into blocks.
After the stencil is computed for each block, the \emph{halo}, i.e.\ the boundary region between blocks is exchanged such that each block has the data necessary to compute the stencil again.
\subsection{The \acrfull{ecm}} \subsection{The \acrfull{ecm}}
@ -76,7 +81,7 @@ Fibrous collagen networks and their viscoelasticity.
\acrshort{ecm} viscoelasticity has been established as an important factor in cell behavior~\cite{chaudhuri2020}. \acrshort{ecm} viscoelasticity has been established as an important factor in cell behavior~\cite{chaudhuri2020}.
For example, the \acrshort{ecm} confines cells and restricts processes such as migration, spreading, growth and mitosis. For example, the \acrshort{ecm} confines cells and restricts processes such as migration, spreading, growth and mitosis.
These processes also affect the \acrshort{ecm} and can lead to permanent deformation. These processes also affect the \acrshort{ecm} and can lead to permanent deformation.
In turn, this deformation can have an influence on cell behavior, resulting in self-reinforcing effects (see for example~\cite{mierke2021}). In turn, this deformation can have an influence on cell behavior, resulting in a string coupling between the behavior of the \acrshort{ecm} and the behavior of the cells.
\subsection{Models of the \acrshort{ecm} in the \acrshort{cpm}} \subsection{Models of the \acrshort{ecm} in the \acrshort{cpm}}
@ -94,7 +99,7 @@ This approach is used for example in~\cite{bauer2007}, where the \acrshort{ecm}
\paragraph{Hybrid \acrshort{cpm}-\acrshort{fem}} \paragraph{Hybrid \acrshort{cpm}-\acrshort{fem}}
An approach using a \acrfull{fem} is presented in~\cite{vanoers2014} and expanded upon in~\cite{rens2017, rens2019}. An approach using a \acrfull{fem} is presented in~\cite{vanoers2014} and expanded upon in~\cite{rens2019, rens2017}.
Each lattice site is assigned a local directional strain on the \acrshort{ecm}. Each lattice site is assigned a local directional strain on the \acrshort{ecm}.
Cells exert traction forces on the \acrshort{ecm} used to calculate the lattice strains by a \acrshort{fem}. Cells exert traction forces on the \acrshort{ecm} used to calculate the lattice strains by a \acrshort{fem}.
The hamiltonian of the \acrshort{cpm} is modified such that cells respond to the strain. The hamiltonian of the \acrshort{cpm} is modified such that cells respond to the strain.
@ -110,7 +115,7 @@ However, in this work, cells interact with the \acrshort{ecm} only through a spa
The strain response of the collagen networks in the \acrshort{ecm} is not fully elastic. The strain response of the collagen networks in the \acrshort{ecm} is not fully elastic.
It exhibits both elastic (spring-like) and viscuous (damper-like) behavior. It exhibits both elastic (spring-like) and viscuous (damper-like) behavior.
The behavior of such viscoelastic materials is modeled by serial or parallel configurations of springs and dampers~\cite{sengul2021, mierke2021}. The behavior of such viscoelastic materials is modeled by serial or parallel configurations of springs and dampers~\cite{mierke2021, sengul2021}.
The most common configurations for describing viscoelastic solids are The most common configurations for describing viscoelastic solids are
\begin{itemize} \begin{itemize}
@ -120,7 +125,8 @@ The most common configurations for describing viscoelastic solids are
\end{itemize} \end{itemize}
Depending on the specific viscoelastic characteristics that are to be predicted, a particular model can be chosen. Depending on the specific viscoelastic characteristics that are to be predicted, a particular model can be chosen.
In order to align the viscoelastic \acrshort{ecm} model with the \acrshort{cpm}, we researched approaches that model viscoelastic materials on square lattices. In order to align the viscoelastic \acrshort{ecm} model with the \acrshort{cpm}, we consider approaches that model viscoelastic materials on square lattices.
In particular, the following approaches might be relevant.
\paragraph{Discrete Particle Method} \paragraph{Discrete Particle Method}
@ -129,7 +135,7 @@ This work extends the discrete particle method for elastic solids presented in~\
It is based on a two- or three-dimensional square lattice of particles. It is based on a two- or three-dimensional square lattice of particles.
Each particle is connected to all of its cardinal and diagonal neighbors. Each particle is connected to all of its cardinal and diagonal neighbors.
The model for the force acting between two particles can be elastic or viscoelastic. The model for the force acting between two particles can be elastic or viscoelastic.
Various models are explored in~\cite{obrien2008, obrien2009, obrien2014, obrien2021}. Various models are explored in~\cite{obrien2008, obrien2014, obrien2021, obrien2009}.
\paragraph{\acrfull{lbm}} \paragraph{\acrfull{lbm}}
@ -144,13 +150,16 @@ In this work we will explore lattice-based viscoelastic simulations of the \acrs
\subsection{Method} \subsection{Method}
For the \acrshort{cpm} we use the distributed implementation \acrshort{cis}.
\acrshort{cis} is based on the \acrshort{nastja} framework implemented using the \acrshort{mpi}, which we will use to develop our model of the \acrshort{ecm}.
The model will likely be based on the viscoelastic discrete particle method, as preliminary experiments based on a simplified implementation show promising results.
In order to model cell-matrix interactions, we will develop a method that allows cells to influence the \acrshort{ecm} simulation. In order to model cell-matrix interactions, we will develop a method that allows cells to influence the \acrshort{ecm} simulation.
To model matrix-cell interactions, we will expand the Hamiltonian of the \acrshort{cpm} to include a term dependent on the local configuration of the \acrshort{ecm}. To model matrix-cell interactions, we will expand the Hamiltonian of the \acrshort{cpm} to include a term dependent on the local configuration of the \acrshort{ecm}.
This should make it possible for our model to simulate the self-reinforcing interactions of cells and \acrshort{ecm}. This should make it possible for our model to simulate the strong coupling of cells and \acrshort{ecm}.
I will explore which of the models listed above is the most promising and compare to them to existing approaches.
For the \acrshort{cpm} we use the distributed implementation \acrshort{cis}.
\acrshort{cis} is based on the \acrshort{nastja} framework implemented using \acrshort{mpi}, which we will use to develop our model of the \acrshort{ecm}.
In order to reduce simulation times we will employ implementation techniques such as \acrshort{gpu} programming.
As the implementation performance of our model will depend on several interconnected factors such as cache efficiency, network latency and \acrshort{gpu} communication cost we will need to benchmark it on a common test setup.
\subsection{Challenges} \subsection{Challenges}
@ -178,7 +187,9 @@ We will experiment with these techniques and evaluate the possible improvements.
\newpage \newpage
\begin{refcontext}[sorting=nyt]
\printglossary[type=\acronymtype, nogroupskip] \printglossary[type=\acronymtype, nogroupskip]
\end{refcontext}
\printbibliography{} \printbibliography{}