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