152 lines
8.2 KiB
TeX
152 lines
8.2 KiB
TeX
\documentclass[a4paper]{article}
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\usepackage[utf8]{inputenc}
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\usepackage[style=numeric]{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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\addbibresource{references.bib}
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\makeglossaries{}
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\newacronym{cis}{CiS}{Cells in Silico}
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\newacronym{cpu}{CPU}{Central Processing Unit}
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\newacronym{cpm}{CPM}{Cellular Potts Model}
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\newacronym{ecm}{ECM}{Extracellular Matrix}
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\newacronym{fem}{FEM}{Finite Element Method}
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\newacronym{gpu}{GPU}{Graphics Processing Unit}
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\newacronym{lbm}{LBM}{Lattice Boltzmann Method}
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\newacronym{mcs}{MCS}{Monte-Carlo Step}
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\newacronym{mpi}{MPI}{Message Passing Interface}
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\newacronym{nastja}{NAStJA}{Neoteric Autonomous Stencil code for Jolly Algorithms}
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\newacronym{sls}{SLS}{Standard Linear Solid}
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\begin{document}
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\title{Exposé}
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\author{Paul Brinkmeier}
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\date{July 2023}
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\maketitle
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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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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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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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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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\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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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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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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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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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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\subsection{The \acrfull{ecm}}
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The \acrshort{ecm} is the part of a tissue that surrounds the cells.
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It provides their physical and biochemical environment, thereby influencing cell behavior~\cite{frantz2010}.
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While the \acrshort{ecm} consists of a variety of components, we focus on a single essential component:
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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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\subsection{Models of the \acrshort{ecm} in the \acrshort{cpm}}
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In this section we list current approaches to modeling the \acrshort{ecm} in \acrshort{cpm} simulations.
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We focus on approaches that explicitly model the plasticity of \acrshort{ecm} collagens.
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\paragraph{Static Cell}
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A starting point is to model the \acrshort{ecm} as a static cell.
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In this model, a cell ID is chosen to represent the solid parts of the \acrshort{ecm}.
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Cell-matrix interactions are regulated by the hamiltonian just like cell-cell interactions.
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\acrshort{ecm} lattice sites do not copy their neighbors and can not be copied by their neighbors during a \acrshort{mcs}.
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Instead, simulations using this approach usually allow cells to degrade adjacent matrix sites over time.
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This approach is used for example in~\cite{bauer2007}, where the \acrshort{ecm} is initialized by randomly placing fiber bundles across the domain and~\cite{scianna2013}, which investigates cell behavior in \acrshortpl{ecm} with regular patterns.
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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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Each lattice site is assigned a local directional strain on the \acrshort{ecm}.
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Cells exert a 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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\paragraph{Hybrid \acrshort{cpm} and Molecular Dynamics Methods}
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Another approach is presented in~\cite{tsingos2022}.
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This work models simulates matrix fibers using a bead-and-chain model.
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Similar to the previous approach, the \acrshort{ecm} model is coupled with the \acrshort{cpm}.
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However, in this work, cells interact with the \acrshort{ecm} only through a sparse subset of lattice sites.
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\subsection{Lattice Models of Viscoelastic Materials}
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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 most common configurations for describing viscoelastic solids are
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\begin{itemize}
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\item the Maxwell model, consisting of a spring and a damper in series,
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\item the Kelvin-Voigt model, consisting of a spring and a damper in parallel
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\item and the Zener or \acrfull{sls} model, which extends either the Maxwell or the Kelvin-Voigt model by another spring.
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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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\paragraph{Discrete Particle Method}
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A model for viscoelastic solids is presented in~\cite{obrien2008}.
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This work extends the discrete particle method for elastic solids presented in~\cite{toomey2000}.
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This model is based on a two- or three-dimensional square lattice of particles.
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Each particle is connected to all of its Moore 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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\paragraph{\acrfull{lbm}}
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The \acrshort{lbm} is an established approach for modeling the dynamics of fluids.~\cite{krueger2017}
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Also based on a square lattice, this model discretizes the particles moving at a particular lattice space into the cardinal and diagonal directions.
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Research suggests that the \acrshort{lbm} can be used for modeling both solids~\cite{maquart2022} and viscoelastic fluids~\cite{malaspinas2010}.
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\section{Contribution}
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\subsection{Method}
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\subsection{Challenges}
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\newpage
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\printglossary[type=\acronymtype, nogroupskip]
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\printbibliography{}
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\end{document}
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