First version of research section in expose
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\documentclass[a4paper]{article}
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\usepackage[
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style=numeric,
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]{biblatex}
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\usepackage[acronym]{glossaries}
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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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@ -17,10 +16,11 @@ style=numeric,
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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 Model}
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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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@ -33,12 +33,12 @@ style=numeric,
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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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One popular model 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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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 \acrfull{ecm} that cells exist in.
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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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@ -52,7 +52,7 @@ The \acrshort{cpm}~\cite{graner1992} models cells as sets of sites on a square l
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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 consists of at 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 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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@ -67,32 +67,74 @@ Since updates happen on a square lattice and changes in energy can be calculated
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\subsection{The \acrfull{ecm}}
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\todo{Sketch the ECM (2 sentences)}
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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~\cite{frantz2010}, we focus on a single essential component:
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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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In the next section we list a few current approaches for modeling the \acrshort{ecm} in the \acrshort{cpm}.
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\subsection{Models of the \acrshort{ecm} in the \acrshort{cpm}}
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% static, constant cellid
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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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% static with degradation
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\paragraph{Static Cell}
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% FEM approach
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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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% network approach (includes viscoelasticity)
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\paragraph{Hybrid \acrshort{cpm}-\acrshort{fem}}
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\subsection{Models of Viscoelastic Materials}
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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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% maxwell, KV, SLS, etc.
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\paragraph{Hybrid \acrshort{cpm} and Molecular Dynamics Methods}
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% ELM
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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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@ -102,7 +144,7 @@ In the next section we list a few current approaches for modeling the \acrshort{
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\newpage
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\printglossary[type=\acronymtype]
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\printglossary[type=\acronymtype, nogroupskip]
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\printbibliography{}
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@ -1,3 +1,33 @@
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@article{scianna2013,
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abstract = {Cell migration on and through extracellular matrix is fundamental in a wide variety of physiological and pathological phenomena, and is exploited in scaffold-based tissue engineering. Migration is regulated by a number of extracellular matrix- or cell-derived biophysical parameters, such as matrix fiber orientation, pore size, and elasticity, or cell deformation, proteolysis, and adhesion. We here present an extended Cellular Potts Model (CPM) able to qualitatively and quantitatively describe cell migration efficiencies and phenotypes both on two-dimensional substrates and within three-dimensional matrices, close to experimental evidence. As distinct features of our approach, cells are modeled as compartmentalized discrete objects, differentiated into nucleus and cytosolic region, while the extracellular matrix is composed of a fibrous mesh and a homogeneous fluid. Our model provides a strong correlation of the directionality of migration with the topological extracellular matrix distribution and a biphasic dependence of migration on the matrix structure, density, adhesion, and stiffness, and, moreover, simulates that cell locomotion in highly constrained fibrillar obstacles requires the deformation of the cell's nucleus and/or the activity of cell-derived proteolysis. In conclusion, we here propose a mathematical modeling approach that serves to characterize cell migration as a biological phenomenon in healthy and diseased tissues and in engineering applications.},
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author = {Marco Scianna and Luigi Preziosi and Katarina Wolf},
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doi = {10.3934/mbe.2013.10.235},
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issn = {15471063},
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issue = {1},
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journal = {Mathematical Biosciences and Engineering},
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keywords = {Cell migration,Cellular Potts model,Extracellular matrix},
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month = {2},
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pages = {235-261},
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pmid = {23311371},
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title = {A cellular potts model simulating cell migration on and in matrix environments},
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volume = {10},
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year = {2013},
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}
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@article{bauer2007,
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abstract = {This work describes the first cell-based model of tumor-induced angiogenesis. At the extracellular level, the model describes diffusion, uptake, and decay of tumor-secreted pro-angiogenic factor. At the cellular level, the model uses the cellular Potts model based on system-energy reduction to describe endothelial cell migration, growth, division, cellular adhesion, and the evolving structure of the stroma. Numerical simulations show: 1), different tumor-secreted pro-angiogenic factor gradient profiles dramatically affect capillary sprout morphology; 2), average sprout extension speeds depend on the proximity of the proliferating region to the sprout tip, and the coordination of cellular functions; and 3), inhomogeneities in the extravascular tissue lead to sprout branching and anastomosis, phenomena that emerge without any prescribed rules. This model provides a quantitative framework to test hypotheses on the biochemical and biomechanical mechanisms that control tumor-induced angiogenesis. © 2007 by the Biophysical Society.},
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author = {Amy L. Bauer and Trachette L. Jackson and Yi Jiang},
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doi = {10.1529/biophysj.106.101501},
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issn = {00063495},
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issue = {9},
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journal = {Biophysical Journal},
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note = {All in all a model that seems very similar to Julians current model plus some blocky ECM cells minus radially aligned fibers},
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pages = {3105-3121},
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pmid = {17277180},
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publisher = {Biophysical Society},
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title = {A cell-based model exhibiting branching and anastomosis during tumor-induced angiogenesis},
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volume = {92},
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year = {2007},
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}
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@article{berghoff2020,
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abstract = {Background: Discoveries in cellular dynamics and tissue development constantly reshape our understanding of fundamental biological processes such as embryogenesis, wound-healing, and tumorigenesis. High-quality microscopy data and ever-improving understanding of single-cell effects rapidly accelerate new discoveries. Still, many computational models either describe few cells highly detailed or larger cell ensembles and tissues more coarsely. Here, we connect these two scales in a joint theoretical model. Results: We developed a highly parallel version of the cellular Potts model that can be flexibly applied and provides an agent-based model driving cellular events. The model can be modular extended to a multi-model simulation on both scales. Based on the NAStJA framework, a scaling implementation running efficiently on high-performance computing systems was realized. We demonstrate independence of bias in our approach as well as excellent scaling behavior. Conclusions: Our model scales approximately linear beyond 10,000 cores and thus enables the simulation of large-scale three-dimensional tissues only confined by available computational resources. The strict modular design allows arbitrary models to be configured flexibly and enables applications in a wide range of research questions. Cells in Silico (CiS) can be easily molded to different model assumptions and help push computational scientists to expand their simulations to a new area in tissue simulations. As an example we highlight a 10003 voxel-sized cancerous tissue simulation at sub-cellular resolution.},
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author = {Marco Berghoff and Jakob Rosenbauer and Felix Hoffmann and Alexander Schug},
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@ -41,10 +71,111 @@
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volume = {29},
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year = {2018},
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}
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@article{vanoers2014,
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abstract = {In vitro cultures of endothelial cells are a widely used model system of the collective behavior of endothelial cells during vasculogenesis and angiogenesis. When seeded in an extracellular matrix, endothelial cells can form blood vessel-like structures, including vascular networks and sprouts. Endothelial morphogenesis depends on a large number of chemical and mechanical factors, including the compliancy of the extracellular matrix, the available growth factors, the adhesion of cells to the extracellular matrix, cell-cell signaling, etc. Although various computational models have been proposed to explain the role of each of these biochemical and biomechanical effects, the understanding of the mechanisms underlying in vitro angiogenesis is still incomplete. Most explanations focus on predicting the whole vascular network or sprout from the underlying cell behavior, and do not check if the same model also correctly captures the intermediate scale: the pairwise cell-cell interactions or single cell responses to ECM mechanics. Here we show, using a hybrid cellular Potts and finite element computational model, that a single set of biologically plausible rules describing (a) the contractile forces that endothelial cells exert on the ECM, (b) the resulting strains in the extracellular matrix, and (c) the cellular response to the strains, suffices for reproducing the behavior of individual endothelial cells and the interactions of endothelial cell pairs in compliant matrices. With the same set of rules, the model also reproduces network formation from scattered cells, and sprouting from endothelial spheroids. Combining the present mechanical model with aspects of previously proposed mechanical and chemical models may lead to a more complete understanding of in vitro angiogenesis.},
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author = {René F.M. van Oers and Elisabeth G. Rens and Danielle J. LaValley and Cynthia A. Reinhart-King and Roeland M.H. Merks},
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doi = {10.1371/JOURNAL.PCBI.1003774},
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issn = {1553-7358},
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issue = {8},
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journal = {PLOS Computational Biology},
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keywords = {Cell motility,Endothelial cells,Extracellular matrix,Extracellular matrix adhesions,Finite element analysis,Monte Carlo method,Simulation and modeling,Stiffness},
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month = {8},
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note = {Looks very promising<br/><br/>Simulates ECM using finite-element model},
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pages = {e1003774},
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pmid = {25121971},
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publisher = {Public Library of Science},
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title = {Mechanical Cell-Matrix Feedback Explains Pairwise and Collective Endothelial Cell Behavior In Vitro},
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volume = {10},
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url = {https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1003774},
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year = {2014},
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}
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@article{tsingos2022,
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author = {Erika Tsingos and Bente Hilde Bakker and Koen A.E. Keijzer and Hermen Jan Hupkes and Roeland M.H. Merks},
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doi = {10.1101/2022.06.10.495667},
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journal = {bioRxiv},
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month = {7},
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publisher = {Cold Spring Harbor Laboratory},
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title = {Modelling the mechanical cross-talk between cells and fibrous extracellular matrix using hybrid cellular Potts and molecular dynamics methods},
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url = {https://www.biorxiv.org/content/10.1101/2022.06.10.495667v3},
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year = {2022},
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}
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@generic{Sree2020,
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abstract = {Growth and remodeling (G&R) of biological tissues is an inherently multiscale and multiphysics process. In the past two decades, computational models of G&R have been developed to improve our fundamental understanding of how tissues adapt to mechanical cues. Models focused on tissue mechanics have successfully captured G&R of tissues but lacking a detailed description of the biological control at the cell level. In contrast, systems biology models of mechanotransduction and cellular processes associated to G&R events have been developed often without coupling to the tissue mechanical behavior at multiple scales. Here, we review novel approaches to fuse the systems biology approach to cell mechanobiology with the continuum mechanics descriptions of G&R.},
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author = {Vivek D. Sree and Adrian B. Tepole},
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doi = {10.1016/j.cobme.2020.01.002},
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issn = {24684511},
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journal = {Current Opinion in Biomedical Engineering},
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keywords = {Multiphysics models,Multiscale models,Systems biology,Tissue mechanics},
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month = {9},
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pages = {75-80},
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publisher = {Elsevier B.V.},
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title = {Computational systems mechanobiology of growth and remodeling: Integration of tissue mechanics and cell regulatory network dynamics},
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volume = {15},
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year = {2020},
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}
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@article{rens2017,
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abstract = {During animal development and homeostasis, the structure of tissues, including muscles, blood vessels, and connective tissues, adapts to mechanical strains in the extracellular matrix (ECM). These strains originate from the differential growth of tissues or forces due to muscle contraction or gravity. Here we show using a computational model that by amplifying local strain cues, active cell contractility can facilitate and accelerate the reorientation of single cells to static strains. At the collective cell level, the model simulations show that active cell contractility can facilitate the formation of strings along the orientation of stretch. The computational model is based on a hybrid cellular Potts and finite-element simulation framework describing a mechanical cell-substrate feedback, where: 1) cells apply forces on the ECM, such that 2) local strains are generated in the ECM and 3) cells preferentially extend protrusions along the strain orientation. In accordance with experimental observations, simulated cells align and form stringlike structures parallel to static uniaxial stretch. Our model simulations predict that the magnitude of the uniaxial stretch and the strength of the contractile forces regulate a gradual transition between stringlike patterns and vascular networklike patterns. Our simulations also suggest that at high population densities, less cell cohesion promotes string formation.},
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author = {Elisabeth G. Rens and Roeland M.H. Merks},
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doi = {10.1016/J.BPJ.2016.12.012},
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issn = {0006-3495},
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issue = {4},
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journal = {Biophysical Journal},
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month = {2},
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pages = {755-766},
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pmid = {28256235},
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publisher = {Cell Press},
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title = {Cell Contractility Facilitates Alignment of Cells and Tissues to Static Uniaxial Stretch},
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volume = {112},
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year = {2017},
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}
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@article{rens2019,
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abstract = {Many animal cells change their shape depending on the stiffness of the
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substrate on which they are cultured: they assume small, rounded shapes in soft
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ECMs, they elongate within stiffer ECMs, and flatten out on hard substrates.
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Cells tend to prefer stiffer parts of the substrate, a phenomenon known as
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durotaxis. Such mechanosensitive responses to ECM mechanics are key to
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understanding the regulation of biological tissues by mechanical cues, as it
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occurs, e.g., during angiogenesis and the alignment of cells in muscles and
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tendons. Although it is well established that the mechanical cell-ECM
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interactions are mediated by focal adhesions, the mechanosensitive molecular
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complexes linking the cytoskeleton to the substrate, it is poorly understood
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how the stiffness-dependent kinetics of the focal adhesions eventually produce
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the observed interdependence of substrate stiffness and cell shape and cell
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behavior. Here we show that the mechanosensitive behavior of single-focal
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adhesions, cell contractility and substrate adhesivity together suffice to
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explain the observed stiffness-dependent behavior of cells. We introduce a
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multiscale computational model that is based upon the following assumptions:
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(1) cells apply forces onto the substrate through FAs; (2) the FAs grow and
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stabilize due to these forces; (3) within a given time-interval, the force that
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the FAs experience is lower on soft substrates than on stiffer substrates due
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to the time it takes to reach mechanical equilibrium; and (4) smaller FAs are
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pulled from the substrate more easily than larger FAs. Our model combines the
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cellular Potts model for the cells with a finite-element model for the
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substrate, and describes each FA using differential equations. Together these
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assumptions provide a unifying model for cell spreading, cell elongation and
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durotaxis in response to substrate mechanics.},
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author = {Elisabeth G. Rens and Roeland M. H. Merks},
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doi = {10.2139/ssrn.3569534},
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journal = {SSRN Electronic Journal},
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month = {6},
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publisher = {Elsevier BV},
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title = {Cell Shape and Durotaxis Follow from Mechanical Cell-Substrate Reciprocity and Focal Adhesion Dynamics: A Unifying Mathematical Model},
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url = {https://arxiv.org/abs/1906.08962v1},
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year = {2019},
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}
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@article{krueger2017,
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author = {Timm Krüger and Halim Kusumaatmaja and Alexandr Kuzmin and Orest Shardt and Goncalo Silva and Erlend Magnus Viggen},
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institution = {Springer International Publishing},
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journal = {Springer International Publishing},
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note = {https://github.com/lbm-principles-practice},
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title = {The lattice Boltzmann method},
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volume = {10},
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year = {2017},
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}
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@article{mierke2021,
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abstract = {Biological materials such as extracellular matrix scaffolds, cancer cells, and tissues are often assumed to respond elastically for simplicity; the viscoelastic response is quite commonly ignored. Extracellular matrix mechanics including the viscoelasticity has turned out to be a key feature of cellular behavior and the entire shape and function of healthy and diseased tissues, such as cancer. The interference of cells with their local microenvironment and the interaction among different cell types relies both on the mechanical phenotype of each involved element. However, there is still not yet clearly understood how viscoelasticity alters the functional phenotype of the tumor extracellular matrix environment. Especially the biophysical technologies are still under ongoing improvement and further development. In addition, the effect of matrix mechanics in the progression of cancer is the subject of discussion. Hence, the topic of this review is especially attractive to collect the existing endeavors to characterize the viscoelastic features of tumor extracellular matrices and to briefly highlight the present frontiers in cancer progression and escape of cancers from therapy. Finally, this review article illustrates the importance of the tumor extracellular matrix mechano-phenotype, including the phenomenon viscoelasticity in identifying, characterizing, and treating specific cancer types.},
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author = {Claudia Tanja Mierke},
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doi = {10.3389/FCELL.2021.785138/BIBTEX},
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doi = {10.3389/FCELL.2021.785138},
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issn = {2296634X},
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journal = {Frontiers in Cell and Developmental Biology},
|
||||
keywords = {cancer,collagen,confinement,extracellular matrix,homogeneities,hydrogels,matrix mechanics,viscoelasticity},
|
||||
@ -55,6 +186,38 @@
|
||||
volume = {9},
|
||||
year = {2021},
|
||||
}
|
||||
@article{malaspinas2010,
|
||||
abstract = {The simulation of viscoelastic fluids is a challenging task from the theoretical and numerical points of view. This class of fluids has been extensively studied with the help of classical numerical methods. In this paper we propose a new approach based on the lattice Boltzmann method in order to simulate linear and non-linear viscoelastic fluids and in particular those described by the Oldroyd-B and FENE-P constitutive equations. We study the accuracy and stability of our model on three different benchmarks: the 3D Taylor-Green vortex decay, the simplified 2D four-rolls mill, and the 2D Poiseuille flow. To our knowledge, the methodology described in this work is a first attempt for the simulation of non-trivial flows of viscoelastic fluids using the lattice Boltzmann method to discretize the constitutive and conservation equations. © 2010 Elsevier B.V.},
|
||||
author = {O. Malaspinas and N. Fiétier and M. Deville},
|
||||
doi = {10.1016/J.JNNFM.2010.09.001},
|
||||
issn = {0377-0257},
|
||||
issue = {23-24},
|
||||
journal = {Journal of Non-Newtonian Fluid Mechanics},
|
||||
keywords = {Lattice Boltzmann method,Viscoelastic fluid flows},
|
||||
month = {12},
|
||||
pages = {1637-1653},
|
||||
publisher = {Elsevier},
|
||||
title = {Lattice Boltzmann method for the simulation of viscoelastic fluid flows},
|
||||
volume = {165},
|
||||
year = {2010},
|
||||
}
|
||||
@article{obrien2021,
|
||||
abstract = {Nonlinear wave propagation is an important consideration in several geophysical problems as heterogeneities within the subsurface give rise to nonlinear stress-strain relationships in rocks. To address these problems, where the inclusion of subsurface complexity is accounted for, numerical solutions are required. Here, we outline a discrete particle or lattice numerical method that can simulate dynamic and static deformation in an isotropic viscoelastic nonlinear medium where the nonlinearity includes the fourth-order elastic tensor coefficients. The relationship between the local interaction constants in the lattice method and the macroscopic nonlinear coefficients is derived and the relationships presented. The theoretical dispersion properties of the system is determined from a nonlinear perturbation method and are validated against some numerical results. There is an excellent agreement between the theory and numerical results and the method reproduces the common features of nonlinear wave propagation, for example, harmonics, waveform distortion and spectra shifts. As expected the system is shown to be dependent on the wave amplitudes and an example is presented which shows the complexity that can arise in both dynamic and static deformation in a complex model where nonlinearity is included.},
|
||||
author = {Gareth S. O'Brien},
|
||||
doi = {10.1093/GJI/GGAA537},
|
||||
issn = {0956-540X},
|
||||
issue = {3},
|
||||
journal = {Geophysical Journal International},
|
||||
keywords = {Computational seismology,Numerical modelling,Wave propagation},
|
||||
month = {1},
|
||||
note = {Not very easy to discern the actual model parameters imo},
|
||||
pages = {1572-1587},
|
||||
publisher = {Oxford Academic},
|
||||
title = {A lattice method for seismic wave propagation in nonlinear viscoelastic media},
|
||||
volume = {224},
|
||||
url = {https://academic.oup.com/gji/article/224/3/1572/5979782},
|
||||
year = {2021},
|
||||
}
|
||||
@article{chaudhuri2020,
|
||||
abstract = {Substantial research over the past two decades has established that extracellular matrix (ECM) elasticity, or stiffness, affects fundamental cellular processes, including spreading, growth, proliferation, migration, differentiation and organoid formation. Linearly elastic polyacrylamide hydrogels and polydimethylsiloxane (PDMS) elastomers coated with ECM proteins are widely used to assess the role of stiffness, and results from such experiments are often assumed to reproduce the effect of the mechanical environment experienced by cells in vivo. However, tissues and ECMs are not linearly elastic materials—they exhibit far more complex mechanical behaviours, including viscoelasticity (a time-dependent response to loading or deformation), as well as mechanical plasticity and nonlinear elasticity. Here we review the complex mechanical behaviours of tissues and ECMs, discuss the effect of ECM viscoelasticity on cells, and describe the potential use of viscoelastic biomaterials in regenerative medicine. Recent work has revealed that matrix viscoelasticity regulates these same fundamental cell processes, and can promote behaviours that are not observed with elastic hydrogels in both two- and three-dimensional culture microenvironments. These findings have provided insights into cell–matrix interactions and how these interactions differentially modulate mechano-sensitive molecular pathways in cells. Moreover, these results suggest design guidelines for the next generation of biomaterials, with the goal of matching tissue and ECM mechanics for in vitro tissue models and applications in regenerative medicine. This Review explores the role of viscoelasticity of tissues and extracellular matrices in cell–matrix interactions and mechanotransduction and the potential utility of viscoelastic biomaterials in regenerative medicine.},
|
||||
author = {Ovijit Chaudhuri and Justin Cooper-White and Paul A. Janmey and David J. Mooney and Vivek B. Shenoy},
|
||||
@ -72,6 +235,87 @@
|
||||
url = {https://www.nature.com/articles/s41586-020-2612-2},
|
||||
year = {2020},
|
||||
}
|
||||
@article{maquart2022,
|
||||
abstract = {This work presents a novel method for simulating the behavior of solid objects with the Lattice Boltzmann Method (LBM). To introduce and validate our proposed framework, comparative studies are performed for computing the static equilibrium of isotropic materials. Remembering that the LBM has strong theoretical foundations in the Boltzmann equation; this latter is firstly adjusted to solid motions, through its Boltzmann-Vlasov special case. This is indeed the case when combined with a suitable mean-field external force term to set a reliable solid framework. Secondly, a library is built and plugged on the top of the well-known Parallel Lattice Boltzmann Solver (PaLaBoS) library. Numerical implementations based on the previous equation of motion for solids are led in a non-intrusive manner so as to present results with an easy and flawless reproducibility. A newly designed Lattice Boltzmann Method for Solids (LBMS) is exhibited through a few key algorithms, showing the overall operation plus the major improvements. Efficiency, robustness and accuracy of the proposed approach are illustrated and contrasted with a commercial Finite Element Analysis (FEA) software. The obtained results reveal considerable potential concerning static and further dynamic simulations involving solid constitutive laws within the LBM formalism.},
|
||||
author = {Tristan Maquart and Romain Noël and Guy Courbebaisse and Laurent Navarro},
|
||||
doi = {10.3390/APP12094627},
|
||||
issn = {2076-3417},
|
||||
issue = {9},
|
||||
journal = {Applied Sciences 2022, Vol. 12, Page 4627},
|
||||
keywords = {Lattice Boltzmann Method for solids,Maxwell equation,Vlasov,field external force term,mean,solid static equilibrium},
|
||||
month = {5},
|
||||
note = {LBM but for solids: Displacements are computed by summing the velocities over time; displacements then apply additional stress in the LBM.},
|
||||
pages = {4627},
|
||||
publisher = {Multidisciplinary Digital Publishing Institute},
|
||||
title = {Toward a Lattice Boltzmann Method for Solids—Application to Static Equilibrium of Isotropic Materials},
|
||||
volume = {12},
|
||||
url = {https://www.mdpi.com/2076-3417/12/9/4627/htm https://www.mdpi.com/2076-3417/12/9/4627},
|
||||
year = {2022},
|
||||
}
|
||||
@article{obrien2014,
|
||||
abstract = {Elastic lattice methods (ELMs) have been shown to accurately model seismic wave propagation in a heterogeneous medium. These methods represent an elastic solid as a series of interconnected springs...},
|
||||
author = {Gareth S. O'Brien},
|
||||
doi = {10.1016/J.CAGEO.2014.03.011},
|
||||
issn = {00983004},
|
||||
journal = {Computers \& Geosciences},
|
||||
keywords = {Computational seismic wave propagation,Discrete particle method,Elastic lattice method},
|
||||
month = {6},
|
||||
pages = {117-124},
|
||||
publisher = {
|
||||
Pergamon Press, Inc.
|
||||
PUB1185
|
||||
Elmsford, NY, USA
|
||||
},
|
||||
title = {Elastic lattice modelling of seismic waves including a free surface},
|
||||
volume = {67},
|
||||
url = {https://dl.acm.org/doi/10.1016/j.cageo.2014.03.011},
|
||||
year = {2014},
|
||||
}
|
||||
@article{obrien2008,
|
||||
author = {Gareth S. O'Brien},
|
||||
doi = {10.1029/2007GL032214},
|
||||
issn = {1944-8007},
|
||||
issue = {2},
|
||||
journal = {Geophysical Research Letters},
|
||||
keywords = {elastic,numerical,seismology,visco,visco&hyphen},
|
||||
month = {1},
|
||||
publisher = {John Wiley & Sons, Ltd},
|
||||
title = {Discrete visco-elastic lattice methods for seismic wave propagation},
|
||||
volume = {35},
|
||||
url = {https://onlinelibrary.wiley.com/doi/full/10.1029/2007GL032214 https://onlinelibrary.wiley.com/doi/abs/10.1029/2007GL032214 https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2007GL032214},
|
||||
year = {2008},
|
||||
}
|
||||
@article{toomey2000,
|
||||
abstract = {A particle-based model for the simulation of wave propagation is presented. The model is based on solid-state physics principles and considers a piece of rock to be a Hookean material composed of discrete particles representing fundamental intact rock units. These particles interact at their contact points and experience reversible elastic forces proportional to their displacement from equilibrium. Particles are followed through space by numerically solving their equations of motion. We demonstrate that a numerical implementation of this scheme is capable of modelling the propagation of elastic waves through heterogeneous isotropic media. The results obtained are compared with a high-order finite difference solution to the wave equation. The method is found to be accurate, and thus offers an alternative to traditional continuum-based wave simulators.},
|
||||
author = {Aoife Toomey and Christopher J. Bean},
|
||||
doi = {10.1046/J.1365-246X.2000.00094.X/2/141-3-595-FIG012.JPEG},
|
||||
issn = {0956540X},
|
||||
issue = {3},
|
||||
journal = {Geophysical Journal International},
|
||||
keywords = {Finite difference methods,Heterogeneity,Particle-based model,Wave propagation},
|
||||
month = {6},
|
||||
pages = {595-604},
|
||||
publisher = {Oxford Academic},
|
||||
title = {Numerical simulation of seismic waves using a discrete particle scheme},
|
||||
volume = {141},
|
||||
url = {https://dx.doi.org/10.1046/j.1365-246x.2000.00094.x},
|
||||
year = {2000},
|
||||
}
|
||||
@article{obrien2009,
|
||||
abstract = {Discrete particle methods or elastic lattice methods represent a 3D elastic solid by a series of interconnected springs arranged on a regular lattice. Generally, these methods only consider nearest neighbour interactions, i.e. they are first-order in space. These interconnected springs interacted through a force term (Hooke's Law for an elastic body), which when viewed on a macroscopic scale provide a numerical solution for the elastodynamic wave equations. Along with solving the elastodynamic wave equations these schemes are capable of simulating elastic static deformation. However, as these methods rely on nearest neighbour interactions they suffer from more pronounced numerical dispersion than traditional continuum methods. By including a new force term, the numerical dispersion can be reduced while keeping the flexibility of the nearest neighbour interaction rule. We present results of simulations where the additional force term reduces the numerical dispersion and increases the accuracy of the elastic lattice method solution. The computational efficiency and parallel scaling of this method on multiple processors is compared with a finite-difference solution to assess the computational cost of using this approach for simulating seismic wave propagation. We also show the applicability of this method to modelling seismic propagation in a complex Earth model. © 2009 Elsevier Ltd. All rights reserved.},
|
||||
author = {Gareth S. O'Brien and Chris J. Bean and Honore Tapamo},
|
||||
doi = {10.1016/J.CAGEO.2008.12.004},
|
||||
issn = {0098-3004},
|
||||
issue = {9},
|
||||
journal = {Computers \& Geosciences},
|
||||
keywords = {Computational seismic wave propagation,Discrete particle method,Elastic lattice method,Numerical seismic dispersion},
|
||||
month = {9},
|
||||
pages = {1768-1775},
|
||||
publisher = {Pergamon},
|
||||
title = {Dispersion analysis and computational efficiency of elastic lattice methods for seismic wave propagation},
|
||||
volume = {35},
|
||||
year = {2009},
|
||||
}
|
||||
@article{graner1992,
|
||||
abstract = {We simulate the sorting of a mixture of two types of biological cells using a modified version of the large-Q Potts model with differential adhesivity. We find long-distance cell movement leading to sorting with a logarithmic increase in the length scale of homogeneous clusters. Sorted clusters then round. We find two successive phases: A rapid boundary-driven creation of a low-cohesivity cell monolayer around the aggregate, and a slower boundary-independent internal rearrangement. © 1992 The American Physical Society.},
|
||||
author = {François Graner and James A. Glazier},
|
||||
@ -87,3 +331,20 @@
|
||||
url = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.69.2013},
|
||||
year = {1992},
|
||||
}
|
||||
@article{sengul2021,
|
||||
abstract = {There are some materials in nature that experience deformations that are not elastic. Viscoelastic materials are some of them. We come across many such materials in our daily lives through a number...},
|
||||
author = {Yasemin Sengül},
|
||||
doi = {10.1098/RSPA.2020.0715},
|
||||
issn = {14712946},
|
||||
issue = {2245},
|
||||
journal = {Proceedings of the Royal Society A},
|
||||
keywords = {nonlinear partial differential equations,solid mechanics,viscoelasticity},
|
||||
month = {1},
|
||||
publisher = {
|
||||
The Royal Society Publishing
|
||||
},
|
||||
title = {Nonlinear viscoelasticity of strain rate type: an overview},
|
||||
volume = {477},
|
||||
url = {https://royalsocietypublishing.org/doi/10.1098/rspa.2020.0715},
|
||||
year = {2021},
|
||||
}
|
||||
|
||||
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